CN101023448A - Imaging system - Google Patents

Abstract

A method and apparatus for reconstruction of a region of interest for an object is provided. The reconstruction of the object may be based on chords which may fill a part, all, or more than all of the region of interest. Using chords for reconstruction may allow for reducing data acquired and/or processing for reconstructing a substantially exact image of the ROI. Moreover, various methodologies may be used in reconstructing the image, such as backprojection-filtration, and modified filtration backprojection.

Description

Imaging system

Quoting of related application

The sequence number that the application requires on February 10th, 2004 to submit to is the rights and interests of the U. S. application of 60/543,331 (examining); And the sequence number that requires on November 24th, 2004 to submit to is the rights and interests of the U.S. Patent application of 60/630,624 (examining).Incorporate sequence number by reference into and be the full content of 60/543,331 U.S. Patent application; Incorporate sequence number by reference into and be the full content of 60/630,624 U.S. Patent application.

Technical field

The present invention relates to method and apparatus to object image-forming.More specifically, part or all that the present invention relates to live body or non-living body inside carried out the method and apparatus of imaging.

The mandate of government

U.S. government has the present invention and pays permission, and have the right under conditional situation, to require the patent owner to give other people, for example fund EB000225 that authorizes according to NIH (NIH) and the relevant provision of EB002765 according to rational clause authorization.

Background technology

Imaging technique generally includes detection from the signal of object and according to detected signal configuration image.The signal that detects can comprise any data that detect from sample, such as electromagnetic signal, magnetic signal, ionization signal, heat and the particle (electronics, proton and neutron etc.) etc. of optional frequency scope.

Any part that can be comprised biological tissue (as human body or animal) or non-living body by the object of imaging.For example, this part can comprise the inside or the outside of object, perhaps comprises the whole outside or the inside of object.Many technology to object image-forming are arranged.The example of imaging technique includes, but is not limited to: computed tomography (CT), positron emission imaging (PET), single photon emission computed tomography (SPECT), magnetic resonance imaging (MRI), electron paramagnetic resonance imaging (EPRI), fluctuation imaging (as phase contrast imaging, thermal acoustic imaging and hot photoimaging), and particle imaging.And various imaging technique can combine, such as, CT imaging and PET imaging can combine the generation image.

CT is a kind of X ray process, and wherein X-ray beam is around movement of objects, photographic images from different perspectives.These images can pass through the computer set cross-sectional image of product body inside altogether.PET is a kind of diagnosing image process, and it can assess the perfusion (perfusion) and the metabolic activity level of the Different Organs system of object (for example human body).Positron camera (layer anlysing photographing device) can be used to produce the cross section tomographic map, this image can be followed the tracks of material (radiopharmaceutical agent) (such as 2-[F-18] Fluoro-D-Glucose (FDG)) according to the radioactivity of emission positron and obtain, and it can be by intravenous injection to object.SPECT scanning and PET scanning all belong to the nuclear imaging category.SPECT scanning can represent such as with the object relevant information of blood flow to tissue.For example, radioactive nucleus can inject by vein, and tissue absorbs these radioactive nucleus (having diseased tissues that different absorption rates is arranged), and the camera of rotation picks up the image of these particles, can pass to computing machine then.These images can be changed and present the cross section on egative film, and can check with 3 dimensional format.In addition, MRI and EPRI imaging are to utilize magnetic field and radio-frequency radiation to produce the imaging technique of information (for example information of Xie Pouing).

For reconstructed image exactly, previous system uses filtered back projection's method (FiltrationBackprojection (FBP) methodology).This method need obtain the data in the whole cross section of object, and needs to handle all data of obtaining, even only need a fraction of image of object, also is like this.For example, if with CT to single breast imaging, then the FBP method need not only comprise this single breast, and comprise second breast the scanning of whole chest region, and trunk etc.This is shown in Fig. 1 a, and Fig. 1 a is the sectional view of sweep test, comprises source, object and detecting device.The FBP method need be obtained the data (as the whole cross section of chest region) that are enough to the imaging of whole cross section.Like this, as shown in Figure 1a, the Shu Bixu in source is enough wide so that whole trunk is exposed to X ray.In addition, as shown in Figure 1a, the detecting device that Previous System uses also must be enough big, to obtain the data of whole chest region.For 3-D view, must scanning object to obtain the data in the whole cross section of object, even only will obtain a fraction of image, also be like this.This comprises second cross section of sweep test shown in Fig. 1 b among Fig. 1 b, it comprises and different source, object and the detecting devices of angle among Fig. 1 a.The system of use FBP method in the past also needs to come reconstructed image to carrying out data processing from the data (as whole chest region) in whole cross section.Particularly, filtered from the data of whole chest region.These requirements of previous FBP algorithm make the processing of obtaining of data and data become difficult.

Summary of the invention

The present invention includes imaging system and obtain the equipment and the method for data.One aspect of the present invention comprises the system and method based on string (chord) reconstructed image.Should can be used for various dissimilar imagings based on the reconstruction of string, these imagings are including (but not limited to) computed tomography (CT), positron emission imaging (PET), single photon emission computed tomography (SPECT), magnetic resonance imaging (MRI), electron paramagnetic resonance imaging (EPRI), tomosynthesis (tomosynthesis), fluctuation imaging (as phase contrast imaging, thermal acoustic imaging and hot photoimaging).Employed string can be filled at least a portion (for example whole) of area-of-interest (ROI) in the reconstruction.ROI can be two dimension, three-dimensional or n dimension.The string that uses in the reconstruction can be the line between 2, for example the part of straight line or curve.The point of definition string can be based on any aspect relevant with imaging, and its example can include, but is not limited to source track or Cartesian coordinates, and we will introduce in detail below.By at least a portion of ROI (for example whole ROI) is decomposed into string, can be based on this string group reconstructed image.For example, multiple method for reconstructing can be rebuild two dimension or three-dimensional ROI with string, as backprojection-filtration (Backprojection Filtration (BPF)) method, minimum filtered back projection (Minimum Filtration Backprojection (MFBP)) method and filtered back projection (FBP) method.

A kind of application of use string method for reconstructing makes and can be reduced to data and/or the processing that the quite accurate ROI image of reconstruction is obtained.For example, for the ROI littler, can obtain the data lacked more required and rebuild quite accurately, and not need the data of obtaining from whole object support are handled than the whole object support of basic reconstruction than object support.Object support can be defined as such area of space, and portion's object function can be non-zero within it, and is zero at its outside this function.At least the string that limits the part (whole or more than whole) of ROI also can limit less than whole object support.

During obtaining, data use different parameters, for example control in the track in source or source, and the data of obtaining can be less than the required data of whole object support imaging.For example, determine that the source is with respect to the track of object (such as, source movement but object is static, the static but object of which movement in source, or source and object move relative to each other).The movement of objects source of some imaging system by wanting imaging relatively, and by utilizing detecting device detection data to produce data.Data can be used to rebuild the partly or completely image of object subsequently.The source may be based on respect to one of object suitable track (perhaps many suitable tracks) that ROI (area-of-interest) selects.Article one, suitable track (perhaps many suitable tracks) can comprise such track, and one group of string section by track definition is filled this ROI in this track.If many track is suitable, then can from these many tracks, select an optimum trajectory according to some factors, for example make uninterested zone (non-ROI) exposure in source be reduced or minimize, thereby be reduced to the burden of picture.

As another example, at least one characteristic in source is modified and is used for obtaining the few data of the comparison needed data of whole object support imaging.The characteristic in source can be revised during the track of source, perhaps can remain unchanged during the track of source.The source feature that can control or revise comprises any aspect in the source that can influence the signal that is received by detecting device, includes, but is not limited to: range of exposures (as the aperture setting of bundle, the width of bundle, the change of cone-beam scope etc.), the intensity of bundle and the spectrum of bundle distribute.Arbitrary standard that data are obtained is depended in the modification of these characteristics in source, includes, but is not limited to: ROI and/or non-ROI.For example, when the relative object of which movement in source, can change the range of exposures in source, make range of exposures point to ROI substantially and do not point to non-ROI substantially.

The present invention also comprises the method and apparatus of deal with data with reconstructed image.One aspect of the present invention comprises the system and method based on on-fixed coordinate system reconstructed image.In one embodiment, can how to define this on-fixed coordinate system based on source track or source at least in part with respect to object movement.After based on this on-fixed coordinate system reconstructed image, this image can be transformed into fixed coordinate system, such as Cartesian coordinates.In another embodiment, image can be rebuild by the string of source track definition.For example, 2 on the track of source just can define a string.For two dimension or three-dimensional ROI, the some or all of of ROI can be defined by the point on the defined string of source track.Various algorithms comprise filtered back projection (FBP) method, and backprojection-filtration (BPF) method and minimum filtered back projection (MFBP) method can be used for based on the string reconstructed image.

Another aspect of the present invention comprises the method and apparatus based on backprojection-filtration (BPF) reconstructed image.The BPF method can at first to data (as the data of back projection's weighting) back projection, be carried out filtering (for example non-moving becomes filtering (shift-invariant filtering)) to this back projection again by the image in the following two steps reconstruction ROI.The method that has many data to obtain can be used to generate the data of BPF method.And the BPF method can accurately be rebuild the image in the given ROI directly according to comprising simplification scanning (reduced scan) data of blocking (truncation) or not comprising the data of blocking.

Comprising on the other hand of this invention utilizes the quite accurately method and apparatus of reconstructed image of truncated data.In one embodiment, the BPF method can be used quite accurately reconstructed image of the data of blocking.In another embodiment, the MFBP method can be used quite accurately reconstructed image of the data of blocking.MFBP method and existing FBP method are diverse, because similar with the BPF method, this MFBP method allows to rebuild according to the data of blocking.Particularly, the MFBP method can directly accurately be rebuild the interior image of given ROI according to containing the simplification scan-data that blocks.The MFBP method also can be according to not comprising accurately reconstructed image of the data of blocking.

Another aspect of the present invention comprises the method and apparatus that utilizes the redundant data reconstructed image.If the source trajectory generation for rebuild the unnecessary string of ROI (such as, those are not the strings of filling area-of-interest), then these data will be considered to redundant.Not to abandon these redundant datas simply, but can change the characteristic of selecting of (for example improving) image with this redundant data.Can use the characteristic of the image of redundant data modification to include, but is not limited to: noise, deviation (bias), texture, resolution and variance (variance).

The method and apparatus that comprises on the one hand again with positron emission method reconstructed image of the present invention.Data that can tissue sampling are used to carry out the reconstruction based on string.The data of being gathered are regarded as by virtual source along virtual source trajectory generation, the data organization of being gathered can be used for reconstruction based on string.Can use various virtual source tracks.

Description of drawings

Fig. 1 a and 1b show when the scanning trunk when obtaining the data of using in the imaging of using the FBP method, two cross sections of source, object and detecting device.

Fig. 2 a-c show when the scanning trunk when obtaining the data of using in the imaging, three cross sections of source, object and detecting device, wherein the data that obtained are less than the quite accurate required data of image that are used to rebuild whole object support.

Fig. 3 shows the block scheme of exemplary imaging system.

Fig. 4 a shows the chest cross section of (comprising breast), and track is put " C " point from " A ".

Fig. 4 b shows the chest cross section of (comprising breast), and track is put " Z " point from " X ".

Fig. 5 a shows general track

Side view with detector plane.

Fig. 5 b is the general track shown in Fig. 5 a

Side view, show string.

Fig. 6 is the synoptic diagram of fan-beam configuration, and the medium line of fan-beam passes rotation center O.

Fig. 7 a shows the λ that is designated as on the track of connection source ₁And λ ₂2 string section, initial angle are λ _Min, end angle is λ _Max

Fig. 7 b shows by the source track and by the λ shown in Fig. 6 a _MinAnd λ _MaxThe regional Ω that the PI line segment of appointment surrounds _R

Fig. 7 c shows fixed coordinate system, and { its initial point is at the rotation center in source for x, y}; { u, w}, its initial point are at source point, and the source orbital radius is R for rotating coordinate system.

Fig. 8 a-c shows several possible source examples of traces, comprises general helical trajectory, circular arc-straight path and two circular arc line track respectively.

Fig. 9 a-c shows three figure that the data in the fan-beam scanning with permanent opening angle are obtained.

Figure 10 a-c show with the figure shown in Fig. 9 a-c similarly, have three figure that the data in the fan-beam scanning of angular aperture of variation are obtained.

Figure 11 a-b shows two track while scans, and the angular range of covering is [π, 2 π] and [1.2 π, 1.8 π], and area-of-interest to be rebuild has been indicated in the shadow region.

Figure 12 a shows and utilizes [π, 2 πs] of fan-beam in Figure 11 a with permanent opening angle to go up the data of gathering.

Figure 12 b shows the image that utilizes the data shown in Figure 12 a and filtered back projection's method to rebuild based on the PI line segment.

Figure 12 c shows the reconstructed image that the image transitions of rebuilding among Figure 12 b is shown behind the fixed coordinate system.

Figure 12 d shows the noise image of rebuilding at the image of rebuilding in Figure 12 c.

Figure 13 a shows and utilizes [π, 2 πs] of fan-beam in Figure 11 a with variation angular aperture to go up the data of gathering.

Figure 13 b shows the image that utilizes data shown in Figure 13 a and backprojection-filtration method to rebuild based on the PI line segment.

Figure 13 c shows the reconstructed image that the image transitions of rebuilding among Figure 13 b is shown behind the fixed coordinate system.

Figure 13 d shows the noise image of rebuilding at the image of rebuilding in Figure 13 c.

Figure 14 a shows and utilizes [1.09 πs, 1.91 πs] of fan-beam in Figure 11 a with variation angular aperture to go up the data of gathering.

Figure 14 b shows the image that utilizes data shown in Figure 14 a and backprojection-filtration method to rebuild based on the PI line segment.

Figure 14 c shows the reconstructed image that the image transitions of rebuilding among Figure 14 b is shown behind the fixed coordinate system.

Figure 14 d shows the noise image of rebuilding at the image of rebuilding in Figure 14 c.

Figure 15 a-c shows that columniform object is scanned with helical source trajectory and corresponding reconstructed image.

Figure 16 shows object support and source track, shows supporting section (x _c∈ [x _S1, x _S2]) and the section (x of back projection _c∈ [x _C1, x _C2]).

Figure 17 a shows two arc tracks, and wherein the surface is by fixing s _a=0.04 π p _Cc, and by scanning s _bBy interval [0,3 π p _Cc/ 2] produce.

Figure 17 b shows the image of the Shepp-Logan model of rebuilding based on the string that comprises the surface shown in Figure 17 a (phantom).

Figure 17 c shows along the string image (solid line) of the reconstruction of the string shown in Figure 17 a and the overview of true picture (dotted line).

Figure 18 a-b shows respectively according to the noiseless 3-PI data of utilizing string to produce and (Figure 18 a) and noise 3-PI data (Figure 18 b) are arranged, uses the image of the Shepp-Logan model that the backprojection-filtration method rebuilds.

Figure 19 a-b shows respectively according to the 3-PI data of utilizing string to produce and (Figure 19 a) and noise 3-PI data (Figure 19 b) are arranged, uses the image of the Shepp-Logan model that minimum filtered back projection method rebuilds.

Figure 20 a-b shows respectively according to the data that produce based on the PI line segment and (Figure 20 a) and noise data (Figure 20 b) is arranged, uses the image of the Shepp-Logan model that the backprojection-filtration method rebuilds.

Figure 21 a-b shows respectively according to the data that produce based on the PI line segment and (Figure 21 a) and noise data (Figure 21 b) is arranged, uses the image of the Shepp-Logan model that minimum filtered back projection method rebuilds.

Figure 22 a shows two examples of the fan-beam data of dividing into groups to produce by the line of response (LOR) that will be associated with given check point (A or B) in two-dimensional rectangle PET system.

Figure 22 b shows by spiral path being projected to the track that obtains on the detector surface of PET system.

Figure 23 a shows based on by s ₁=0 and s ₂The image of the Sehpp-Logan model that the string of ∈ (1,3) appointment is rebuild, wherein, display window is [1.0,1.05].

Figure 23 b shows based on by s ₁=0.5 and s ₂The image of the Sehpp-Logan model that the string of ∈ (2,3) appointment is rebuild, wherein, display window is [1.0,1.05].

Figure 24 a-c shows respectively at x=0cm, y=-2.7cm, and the image in the plane of z=2.5cm, display window are [1.0,1.05].

Figure 25 a shows the required scanning angle range lambda of accurate reconstruction image ₁To λ ₂

Figure 25 b shows the actual scanning angular range λ of expression redundant information _MinTo λ _Max

Embodiment

In order to solve the deficiencies in the prior art, the method and apparatus to object image-forming will be described below.Can be to object image-forming based on a part of filling area-of-interest (ROI) at least (, perhaps manys') string as all.ROI can be two-dimentional, three-dimensional or the n dimension.Rebuild employed string and can be the line between 2, such as the part of straight line or curve.The point of definition string can be based on any aspect relevant with imaging, and its example can include, but is not limited to the track or the Cartesian coordinates in source, will tell about in detail below.By at least a portion of ROI (for example whole ROI) is decomposed into string, can be based on this string group and reconstructed image.For example, comprise backprojection-filtration (BPF) method, minimum filtered back projection (MFBP) method and filtered back projection (FBP) method as the whole bag of tricks that can use string to rebuild two dimension or three-dimensional ROI.For example, will fill the accurately reconstruct of difference on the string of at least a portion (perhaps whole) of ROI, with to this ROI imaging.

Using an application of string reconstruction method is the amount that can reduce the data of obtaining and/or handling for the image of quite accurately rebuilding ROI.For example, the ROI littler than object support can quite accurately be rebuild by obtaining than the required data of lacking of the whole object support of basic reconstruction, and do not need to handle the data of obtaining from whole object support.Object support can be defined as such area of space, and portion's object function can be non-zero within it, and is decided to be zero at its outside this function one.Discuss in more detail as following, the example that two-dimensional bodies support comprises the cross section of chest, zone in the inside, chest cross section constitutes object support (it can have the non-zero value), and the part of outside, cross section is positioned at (it necessarily has nonzero value) outside the object support.If ROI only comprises the part of object support, such as the cross section of a breast in the torso portion, then can obtain and handle the data of lacking than the data that are used for whole object support, with the cross section of reconstructive breast quite accurately.For example, can be used for the cross section of accurate reconstruction breast with the relevant data of supporting section of definition ROI.Supporting section can be defined as such string, and its value on each section can be non-zero, but the value one of object function is decided to be zero outside section.Therefore, different with former method, in order accurately to rebuild ROI, only need to obtain the data relevant with supporting section, rather than the data of whole object support.Similarly, the example that three-dimensional body supports comprises the part of trunk, such as the volume from the stomach to the neck.If ROI comprises the sub-volumes of this object support,,, can obtain and handle than rebuilding the required data of lacking of whole object support then in order quite accurately to rebuild the volume of this breast as the volume of a breast in the torso portion.In this three-dimensional example, obtain the data of lacking than whole trunk for the volume of the single breast of imaging.For example, for this single breast of imaging, can obtain the data relevant with the supporting section that defines breast volume.

String can be used to define at least a portion (all, perhaps more) of ROI.In addition, string can be used for definition less than whole object support.The various parameters of utilizing data to obtain such as the control of source track, source or detecting device etc., can be obtained the few data of the comparison needed data of whole object support imaging.For example, when seeking two-dimensional section quite accurately rebuild, if only seek the image in a part of cross section, then the method and apparatus of one aspect of the present invention does not need that data are carried out in whole contiguous cross section and obtains.Similarly, when carrying out the rebuilding quite accurately of three-D volumes, iff carrying out imaging to the part of object support, then the method and apparatus of one aspect of the present invention need not carry out data at whole volume and obtains.

In the accompanying drawings, the similar similar parts of designated, Fig. 2 a shows the cross section of source 312, object 316 and detecting device 320.Will describe in detail as following, the source can be along the track of being indicated by the dotted line among Fig. 2 a with respect to object of which movement.The part 204 in whole cross section 206 is to wish (shown in the thick line) quite accurately rebuild.In the former imaging system, need ask the data that obtain q.s to come the whole cross section 206 of imaging.Thereby the source track also must be enough to obtain the data that are used for whole cross section, as surrounding the track in cross section 206.Different some place on track, source 312 need have wide to enough bundles in the whole cross section 206 of covering.In addition, detecting device 320 also must be enough big, so that the data of registration from point " A " to point " B ".In addition, if only there is part 204 to need accurate reconstruction, then the data from point " A " to point " B " also must be through handling (at least partially).

Comparatively speaking, in one aspect of the invention,, then can only obtain the data that the data of imaging will be lacked to be carried out (it comprises part 204 and other parts) in whole cross section 206 than being enough to if having only part 204 to need to rebuild fully.Will go through as following, if just will rebuild 204 parts, then the whole bag of tricks (such as backprojection-filtration (BPF) method and minimum filtered back projection (MFBP) method) does not need to be enough to data that imaging is carried out in whole cross section 206.But, can use the data of the data that imaging is carried out in whole cross section 206 being lacked than being enough to.For example, can only use the data that are enough to 204 parts are carried out imaging, such as the data of the supporting section that defines 204 parts.

Owing to only need the data the data of whole cross section imaging lacked than being enough to,, and can be different from former imaging system so many aspects that data are obtained (for example the choosing of track, to the control of source or detecting device etc.) can correct.Such as, can select the relevant path in source, this track obtains than being enough to the data that the data of imaging are lacked is carried out in whole cross section.Shown in Fig. 2 a, this track is semicircular, with one group of string of produce filling 204 parts (following also will discuss in more detail).These string groups can be defined as supporting section, because if surpassed supporting section, then the object function is zero.This track that surrounds cross section 206 fully with prior art is different.Track shown in Fig. 2 a only is an example.Also can use other track, will discuss in more detail below.For example, can use greater than the semicircle track shown in Fig. 2 a but less than the track of 360 ° of tracks.Like this, can obtain the data that the data of imaging are lacked to be carried out in whole cross section than being enough to.Similarly, seeking under the 3-D view situation, image if desired is littler than whole three-D volumes, then can obtain than being enough to whole three-D volumes to be carried out the data that the data of imaging are lacked.

As another example, the source can be changed so that the data of detector acquisition are lacked than the data that are enough to the imaging of whole cross section.For example, can be, make the data of acquisition be enough to imaging at least, but be not enough to the imaging of whole cross section to ROI with the characteristic changing in source.Any characteristic that can revise the source is to influence the detected data of detecting device.As following will be discussed in detail, the example characteristic comprises range of exposures (aperture as bundle is set, the width of bundle, the change of cone-beam scope etc.), the intensity of bundle and the spectrum distribution of bundle etc.Such as, can change the width of the bundle in source, cover whole 204 parts so that restraint.Detecting device 320 can obtain the data between 2 points " C " and " D " like this.Alternatively, the beam width in source can be in following scope, and this scope still comprises 204 parts (for example, more than or equal to the width of putting " D " point from " C ") less than whole cross section (such as less than the width of putting " B " point from " A ").For example, beam width can obtain data for making detecting device 320 between point " E " and point " F ".

When source during with respect to object of which movement, it is constant that the characteristic in source can keep, and perhaps can change.For example, it is constant that the characteristic in source can keep, so that the data of obtaining are enough to the imaging to ROI at least, but is not enough to the imaging of whole cross section.Perhaps, the characteristic in source can change once during track at least, so that the data of obtaining are enough to the imaging to ROI at least, but is not enough to the imaging of whole cross section.Fig. 2 b shows the sectional view of source 312, object 316 and detecting device 320, wherein, source 312 compare among Fig. 2 a not in same position.Will go through as following, can select the characteristic in source according to selected ROI.Shown in Fig. 2 b, the width that can increase or reduce to restraint is so that bundle comprises ROI at least.Perhaps, beam width can be selected, but width is not enough to cover whole cross section 206 so that it comprises ROI.Any one aspect of Controlling Source can reduce the irradiation to object, but still sufficiently illuminated portion 204 to carry out imaging.Such as, the data that still can obtain supporting section are controlled in the source, this supporting section can comprise part 204.

Because these methods do not need to be enough to data that whole cross section or whole volume are carried out imaging, so the data that can obtain to block (such as, than being enough to that the data that imaging is lacked or can be carried out truncation part to the data of imaging are carried out in whole cross section).For example, shown in Fig. 2 c, detecting device is depicted as from point " G " and is cross over point " H ", wherein comprises the data about ROI between point " C " and the point " D ".Under the method for prior art, detecting device 320 must be greatly to obtaining the data that are enough to the imaging of whole cross section.On the contrary, the detecting device 320 shown in Fig. 2 c can be littler, so that the portion of the blocking imaging of pair cross-section.In addition, can obtain the data (for example, being less than the data that are enough to whole cross section is carried out imaging) of reduction.Littler detecting device has superiority because it manufacture more cheap and/or, if detecting device is designed in the process that data are obtained to move, then need energy still less to move.

As discussed above, former method has been obtained extra data, and these extra data are not that quite accurately to rebuild ROI necessary.These extra data can not be improved the reconstruction of ROI, also can reduce reconstruction quality.For example, if with in the relevant data of the object support of the outside of ROI, have motion or noise, if then use these data to rebuild ROI, will make image deterioration.

Another aspect of the present invention is a deal with data to produce the method and apparatus of image (such as, quite accurate image).In one embodiment, the reconstruction of image is that at least a portion ground carries out based on string.The part of ROI, all or manyly can resolve into string.String can utilize the connection (such as straight line or curve) between these 2 to define by 2.For example, whole two dimension or three-dimensional ROI district can define with one group of string.ROI can rebuild based on described string, rebuilds such as the section pointwise ground along string.

The string that is used to rebuild can be defined by any aspect relevant with imaging.Such as, two end points that can define a string can will discuss in more detail below based on the source track.As another example, string also can define by Cartesian coordinates.The whole bag of tricks that comes reconstructed image based on the string of source track definition be can use, FBP, BPF and MFBP comprised.In another embodiment, the reconstruction of image can be based on the data (for example, when a part of imaging of pair cross-section, can use the data that are not enough to the imaging of whole cross section) that are not enough to entire portion is carried out imaging.Can use underutilization the data of entire portion imaging are come the whole bag of tricks of reconstructed image, these methods include, but is not limited to BPF and MFBP.

Fig. 3 shows the block scheme of imaging system 300 according to an embodiment of the invention.This system can comprise the imaging system of any kind.The example of imaging system type includes, but is not limited to: computed tomography (CT), positron emission imaging (PET), single photon emission computed tomography (SPECT), magnetic resonance imaging (MRI), electron paramagnetic resonance imaging (EPRI), tomosynthesis (such as using track to create the situation of passing the string for the treatment of imaging moiety, discussing as following) and fluctuation imaging (such as phase contrast imaging, thermal acoustic imaging and hot photoimaging).And these imaging systems can comprise imaging or polytype imaging of single type.Such as, imaging system can comprise the CT imaging.Alternatively, this imaging system can comprise polymorphic imaging, such as the combination of CT and PET imaging.In addition, this imaging system can be used with other system in combination.For example, this imaging system can combine with therapy system (such as the radiation-therapy delivery system).These two systems can be like this in conjunction with work, and imaging system provides and instructs with imaging (as the CT imaging), and radiation-therapy provides treatment.

With reference to Fig. 3, realize that exemplary imaging system 300 of the present invention comprises the general calculation device of computing environment 302 forms, computing environment 302 comprises processing unit 304, system storage 306 and display 308.System bus 310 can connect each system component of computing environment 302, comprises processing unit 304, system storage 306 and display 308.By access system memory 306, processing unit 304 can be carried out arithmetic operator, logical operation and/or control operation.For example, processing unit 304 can be controlled different system components obtaining the data that are used for imaging, and can handle the data obtained to generate image.Alternatively, different system processors or different devices can be controlled different system components obtaining the data that are used for imaging, and can handle the data obtained to generate image.

System storage 306 can store information and/or the instruction that is used in combination with processing unit 304.For example, system storage 306 can storage computation machine instructions, data structure, program module etc., be used for the operation of imaging system 300, this operation is discussed as following such as any motion control and the control of the function of source and detecting device that comprises in source, object and the detecting device.In addition, system storage 306 can be stored the data that obtain from detecting device 320, and can handle the data that are used to be presented on the display 308, can discuss in more detail below.System storage 306 can comprise volatile memory and nonvolatile memory, such as random-access memory (ram) and ROM (read-only memory) (ROM).It should be appreciated by those skilled in the art, can store and also can be used for this illustrative computer environment by the computer-readable medium (such as tape, flash card, random access memory, ROM (read-only memory) etc.) of other type of the data of computer access.Discuss as following, the user can will order and/or information is input in this computing environment 302 by unshowned input media (such as mouse and keyboard).These orders and/or information can be used for the control operation of imaging system, and this control operation comprises the processing with data of obtaining of data.

Fig. 3 has also shown the source 312 of communicating by letter with computing environment 302 by circuit 314.Circuit 314 can comprise control line, by this control line, and at least one characteristic that processing unit can Controlling Source 312.The controllable characteristics in source comprises any aspect in source, and these aspects include, but is not limited to: the intensity of range of exposures (as the setting of beam orifice, the width of bundle, the change of cone-beam scope etc.), bundle and the spectrum of bundle distribute.Source 312 can be static, perhaps can with respect in object 316 or the detecting device 320 one or two and move.Such as by order is sent to the motor (not shown) so that the some or all of of source 312 moves the motion that circuit 314 also can Controlling Source 312.For example, if source 312 is X-ray tubes, then motor can make whole X-ray tube with respect to one or two motion in object 316 and the detecting device 320.Alternatively, it is static that X-ray tube can keep, simultaneously with the rotation of motor-driven reverberator.Like this, can move the bundle of launching from X-ray tube by the bounce-back of reverberator halved tie of rotation.

Source 312 can comprise any device of any signal that generation detecting device 320 can receive.Can be dependent on the type of the imaging of being undertaken by imaging system 300 for the source 312 of imaging system 300 selections.For example, source 312 can produce the electromagnetic radiation of any frequency range, such as, gamma ray, X ray, visible light, microwave and radio or television ripple.Particularly, source 312 can comprise x-ray source and produce X ray, perhaps can comprise radio frequency (RF) source and produce radiowave.Source 312 can also produce the signal of other type, as magnetic field, mechanical wave (as, sound wave), heat, particle (as, electronics, proton, neutron) etc.Although be described in imaging system 300, the imaging system of some type does not need source (such as source 312).For example, PET scanning does not need external source, will go through below.

Fig. 3 also shows object 316.Object 316 can comprise anything that can be scanned, such as biological tissue (as people or animal) or non-living body object (as, luggage, container, food, ocean, inferior).The position of object can be static, perhaps can be with respect to one of source 312 and detecting device 320 or both motions.Such as by sending a command to mobile object 316 to the motor (not shown), circuit 318 can be controlled the motion of object 316.The arbitrary some or all of of object 316 can come imaging with imaging system 300.And a material can be swallowed or be injected into to object, and such as contrast medium, it can assist the some or all of imaging to object 316.As shown in Figure 3, source 312 is in object 316 outsides.Alternatively, source 312 can be in the inside of object 316.

Also show among Fig. 3 by circuit 324 and 326 detecting devices 320 of communicating by letter with computing environment 302.Circuit 324 can comprise control line, by this control line, and at least one characteristic that processing unit can control detection device 320.The controllable characteristics of detecting device comprises any aspect of detecting device, and these aspects include, but is not limited to: the activation/inactivation of the part 322 of detecting device or the sensitivity of detecting device.Circuit 326 can comprise data line, and by this data line, the data that detecting device detects can be sent to computing environment 302, handles for processing unit 304, below also can discuss.Detecting device 320 can comprise the detecting device of any kind that detects arbitrary data, and described arbitrary data is such as the electromagnetic radiation (as X ray) of optional frequency scope, magnetic field, sound wave, warm etc.For example, for two-dimensional detector (flat-panel imager), detecting device 320 can comprise: aim at the four lines detecting device of fan-beam geometric configuration or at the detecting device more than four lines of cone-beam geometric configuration at delegation's detecting device of fan-beam geometric configuration, pin.Detecting device 320 can be static, perhaps can be with respect to one of source 312 and object 316 or both motions.Such as coming the some or all of of moving detector 320 by send order to the motor (not shown), the motion that circuit 324 can control detection device 320.As shown in Figure 3, detecting device 320 is in the outside of object 316.Alternatively, detecting device 320 can be in the inside of object 316.Thereby source 312 and detecting device 320 boths can be in the inside or the outsides of object.In addition, source 312 can be in the inside of object 316 and detecting device 320 in object 316 outsides; Perhaps source 312 can be in the outside of object 316 and detecting device 320 in object 316 inside.For example, can and place the detector acquisition patient's of patient's mouth tooth image by external source.

Based on one in source 312, object 316 and the detecting device 320, several or whole move the various scannings that can produce to object.For example, by when making source 312 and detecting device 320 maintenances static, allowing object 316 translations, can produce rectilinear scanning.As another example,, can produce circular arc scanning by synchronous rotational source 312 and detecting device 320 when making object 316 maintenances static.In another example,, can produce spiral scan by synchronous rotational source 312 and detecting device 320 when making object 316 translations.Rectilinear scanning, circular arc scanning and spiral scan all only are exemplary.Also can produce other scanning, will go through below.

Object 316 can comprise by the area-of-interest of imaging system 300 imagings (ROI).This ROI can comprise the two-dimensional section of object or can be the three-D volumes of object.For example, two dimensional image can comprise projection or cross section picture.As another example, 3-D view can comprise sagittal image (sagittal image) or crown image (coronal image).And, ROI can be object 316 single part, a plurality of some or all of.For example, ROI can be the overall volume of single breast (left side or right breast), perhaps can be the overall volume of left breast and right breast.Alternatively, ROI can be the cross section of single breast.

The imaging selection of track

As mentioned above, common imaging system need be obtained the data of whole object support and need handle all data of obtaining, even only need a fraction of image of object support, also is like this.In one aspect of the invention; the a fraction of image of object support is (such as ROI if desired; it is the part of cross section or volume); then can select the relevant path in source; this track obtain than be enough to whole object support (such as; whole cross section or whole volume) the few data of data of imaging, but this track obtains the data that are enough at least the ROI imaging.For example, use common imaging system,, track is chosen as surrounds whole chest region fully if ROI is single breast.For example, if what use is spiral scan, then the source will around chest region rotate complete 360 ° to obtain data about single breast.A large amount of excessive scanning that this can cause object makes object by unnecessarily excessively irradiation of source 312.If the exposure of restriction source 312 (such as the situation of x-ray source), then this excessive irradiation is debatable.If pay the utmost attention to acquisition speed, then excessively scanning is not wished to occur yet.

In one aspect of the invention, can come the suitable track (or a plurality of suitable track) of selection source according to ROI with respect to object.A suitable track (or a plurality of suitable track) can comprise such track, wherein fills ROI by one group of supporting section of the string of this track definition.If it is suitable that a plurality of tracks are arranged, can from these a plurality of tracks, select optimum trajectory based on some factor so, be discussed below.

ROI can be a two dimension or three-dimensional.An example (cross section of single breast) and the suitable track from point " A " to point " C " of two-dimentional ROI have been shown among Fig. 4 a.Fig. 4 a shows the figure in the chest cross section that comprises breast.The bold curve area surrounded represents to treat the peripheral ROI of imaging.Parallel segment among the ROI is represented supporting section, and these supporting sections are parallel PI line segment parts in ROI.Shown in Fig. 4 a, the object function can be a non-zero along the value of supporting section, but the value outside supporting section must be zero.Point on " A " to " C " track can define string.Particularly, string can be defined as 2 the straight line that connects on the track.In the example shown in Fig. 4 a, " A " point on the track and " C " point have defined a string.Shown in this string " A-C ", at least a portion of string (thick line among Fig. 4 a) is one section that this string passes object to be scanned.If the string section of particular track definition has been filled ROI, then this track is suitable for imaging.

Many group strings can define single ROI.In the two-dimensional example shown in Fig. 4 a, the track of " A " to " C " is suitable, because there is one group of supporting section by the string definition of track, these supporting sections have been filled the area of area-of-interest.For example, shown in Fig. 4 a, one group of each string that all is parallel to " A " to " C " string can be filled area-of-interest.Another example is such one group of string, and first of each string all by the definition of " A " on track point, and second of each string is limited at from point " C " in the scope of point " D ".Another example is such one group of string of filling area-of-interest, and first of each string by the definition of " C " on track point, and second of each string is limited at point " A " on the track in the scope of point " E ".Like this, depend on the point of choosing on the track, organize string more and can fill area-of-interest.

And not only a track is fit to ROI.Another example of the ROI of single breast has been shown among Fig. 4 b, a suitable track from point " X " to point " Z " has wherein been arranged.Similar to the track shown in Fig. 4 a, the track of " X " to " Z " can define one group of string section of the ROI that fills single breast.

Based on single or multiple standards, can from a plurality of suitable tracks, choose a preferred trajectories.The example of described standard includes, but is not limited to: (1) makes the source reduce the irradiation of non-ROI part or minimizes; (2) be lowered into the cost of picture.At first, there are some examples, in these examples, should reduce or minimize the irradiation in source.Such as, in using the CT scan of x-ray source, track can be chosen as, the X ray that makes this source reduces the irradiation in the zone (non-ROI) beyond the area-of-interest or minimizes.Fig. 4 a and 4b provide the examples of traces that is fit to the ROI of single breast.A kind of mode of estimating many suitable tracks is to determine the exposure of source to non-ROI.In the two-dimensional example of Fig. 4 a and 4b, can determine exposure by calculating the area in the ROI zone of being shone by the source (the non-ROI that is shone by the source just) in addition.Two figure relatively arrive the track of " C " with respect to " A ", and the track of " X " to " Z " makes the source shine more non-ROI area.Therefore, according to this independent standard, the track of " A " to " C " is considered to be better than the track that " X " arrives " Z ".

Two-dimensional example shown in Fig. 4 a and the 4b only is used for illustrative purpose.In three dimensional area of interest, can calculate the irradiation of source to the volume (with respect to area) of object.Track with less non-ROI volume is better than having the track of bigger non-ROI volume.In addition, in the given example of Fig. 4 a and 4b, non-ROI area has been given the weight that equates.Yet especially responsive to the irradiation in source if the part of object may be considered to, the source can be calculated by giving bigger weight the irradiation of this sensitivity part of object.For example, owe sensitive portions to the more responsive part of source irradiation with respect to other of this object in the object and can give bigger weight.

In addition, can from many suitable tracks, select a track based on the imaging cost.The example of imaging cost can include, but is not limited to imaging time and imaging capability.For example, can obtain the track of data fast can be more satisfactory than needing the more time to obtain the track of data.As another example, depend on the structure of object, some track may more difficult imaging.

Can select track to scan the ROI of certain objects or can select track to scan the ROI of general object.For example, can select track to scan the right breast of given patient.Like this, track can customize at the shape of the right breast of this given patient, thereby satisfies some factor, minimizes such as the irradiation that makes the source.Alternatively, can select track to scan any patient (perhaps one group of patient's) single breast with specific body weight, height etc.Like this, can be identified for the preferred trajectories of the ROI of general object, this track can be programmed in the imaging system 300 then, thereby not need each patient is recomputated track with logic.In another embodiment, if track is fixed, then this method and system can determine to use this fixing track can to which ROI imaging.Particularly, can determine one or more ROI, its data that can produce through fixation locus motion according to the source are by imaging.For example, for fixation locus, the part that permission supporting section that can recognition object is filled the zone, thus this zone can be by imaging.

It below is the example that can be used for the track of imaging.Make the one-tenth transform in the consideration

Support to be limited in a radius be ρ _s, height is z _sRight cylinder in, and this cylindrical axis is overlapped with the z axle of fixed coordinate system.Can use

The representation space vector, it can be write as in fixed coordinate system $\stackrel{\→}{r}=(x,y,z).$ Therefore, can suppose:

$f\left(\stackrel{\&RightArrow;}{r}\right)=0,x^2+{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">y</figure-callout>}}^2>{\mathrm{\&rho;}}_{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">s</figure-callout>}}^2,z<0,\mathrm{orz}>z_s---\left(1\right)$

Consider the general track while scan that shows among Fig. 4 a and the 4b, suppose that this track is by being the vector of the function of s as path

Portray, but this function implicit definition is:

$\left|\frac{d{\stackrel{\&RightArrow;}{r}}_0\left(s\right)}{\mathrm{ds}}\right|=1---\left(2\right)$

Path provides a parameter, utilizes this parameter can discern point along track.Reconstruction theory discussed in more detail below can utilize the derivative of source along the position of track, and adopts path as parameter, can avoid coordinate singular point (singularity) or many-valued point.In fixing Cartesian coordinates, can remember work: ${\stackrel{\&RightArrow;}{r}}_0\left(s\right)=(x_0\left(s\right),y_0\left(s\right),z_0\left(s\right)).$ Thereby the point on the track is given to the distance of z axle:

$\mathrm{\&rho;}\left(s\right)=\sqrt{x_0^2\left(s\right)+{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">y</figure-callout>}}_0^2\left(s\right)}---\left(3\right)$

And the distance of the point on from the initial point to the track can be given:

$R\left(s\right)=\sqrt{x_0^2\left(s\right)+{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">y</figure-callout>}}_0^2\left(s\right)+{\mathrm{<figure-callout\; id="0"\; label="z"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">z</figure-callout>}}_0^2\left(s\right)}---\left(4\right)$

The detecting device that is denoted as the parts 320 among Fig. 3 is designated as has flat geometry, and supposes and can rotate and translation, so that the line from source point to the detecting device mid point keeps vertical with detector plane.As discussed earlier, detecting device 320 and source 312 can rotate and translation each other.Although detecting device has flat geometry in current example, detecting device 320 can be a curved surface, perhaps can comprise 322 parts, and it can move independently of each other.And source point also can change along with the variation of path apart from S (s) to detector plane.

With reference to figure 5a, show by

The general track of portrayal.R shown in Fig. 5 a (s) (or S (s)) can represent that some s on the track is to the distance of z axle (or detector plane).With reference to figure 5b, show at s _aAnd s _bStraight line (runic) with intersection of locus.This straight line is the example of the string of a musical instrument, and the string of a musical instrument exists

With Between part (shown in black thick line section) can be called as string.General track shown in Fig. 5 a and the 5b comprises limited bending (kink), and these places are non-differentiabilities.Be without loss of generality, suppose s _a≤ s _bThe section of track, s ∈ [s _a, s _b], can be called orbit segment.The direction that can represent the string of a musical instrument with following formula:

${\hat{e}}_c=\frac{{\stackrel{\&RightArrow;}{r}}_0\left(s_b\right)-{\stackrel{\&RightArrow;}{r}}_0\left(s_a\right)}{|{\stackrel{\&RightArrow;}{r}}_0\left(s_b\right)-{\stackrel{\&RightArrow;}{r}}_0\left(s_a\right)|}---\left(5\right)$

Arbitrfary point on the string of a musical instrument

Can be expressed as:

$\stackrel{\&RightArrow;}{r}=\frac{1}{2}[{\stackrel{\&RightArrow;}{r}}_0\left(s_a\right)+{\stackrel{\&RightArrow;}{r}}_0\left(s_b\right)]+x_c{\hat{e}}_c,x_c\&Element;R---\left(6\right)$

In addition, can on the string of a musical instrument at point And the point

Between section be called string.Point on the string

Can be expressed as:

$\stackrel{\&RightArrow;}{r}=\frac{1}{2}[{\stackrel{\&RightArrow;}{r}}_0\left(s_a\right)+{\stackrel{\&RightArrow;}{r}}_0\left(s_b\right)]+x_c{\hat{e}}_c,x_c\&Element;[-l,l].---\left(7\right)$

Wherein, $l=\frac{1}{2}|{\stackrel{\&RightArrow;}{r}}_0\left(s_b\right)-{\stackrel{\&RightArrow;}{r}}_0\left(s_a\right)|$ Half of expression chord length.In the example of helical trajectory, path s and rotation angle λ are proportional, and, work as s _aAnd s _bIn in one curved (one tum), string of a musical instrument chord just can be interpreted as PI line and PI line segment respectively.But, can use the track of other type.And can use the string of other type, such as, many PI lines.

The notion of string can be applied to particular track.For example, the PI line can be used for carrying out fan-beam and scan reconstructed image on the part of circular arc source track, as shown in Figure 6.Particularly, Fig. 6 shows the synoptic diagram of fan-beam structure.The initial angle of source track and end angle are respectively by λ _MinAnd λ _MaxExpression.The center line of fan-beam shown in Figure 6 passes rotation center O, and the distance between source and the detecting device is represented with S.

Shown in Fig. 7 a, the PI line segment is to connect by scan angle λ ₁And λ ₂2 straight-line segment of mark.Use x _πThe coordinate of the point on the expression PI line segment, then (x _π, λ ₁, λ ₂) be the PI line coordinates.Shown in Fig. 7 b by source track and λ _MinAnd λ _MaxThe regional Ω that determined PI line segment surrounds _RAvailable non-intersect PI line segment complete filling.Complete filling zone Ω _RAn example of non-intersect PI line segment be shown as one group of parallel lines among Fig. 7 b.Therefore, regional Ω _REach interior point can belong to and only belong to one of these parallel PI line segments.In addition, (x is y) with PI line coordinates (x for stationary coordinate _π, λ ₁, λ ₂) between relation determine by following formula:

x＝R((1-t)cosλ ₁+tcosλ ₂)，(8)

y＝R((1-t)sinλ ₁+tsinλ ₂)，(9)

Wherein, t ∈ [0,1] and x _πThe pass be:

$x_{\mathrm{\&pi;}}=(t-1/2)|{\stackrel{\&RightArrow;}{r}}_0\left({\mathrm{\&lambda;}}_1\right)-{\stackrel{\&RightArrow;}{r}}_0\left({\mathrm{\&lambda;}}_2\right)|---\left(10\right)$

Therefore, x _πThe mid point of=0 expression PI line segment.In fixed coordinate system, the source track

Can be expressed as:

${\stackrel{\&RightArrow;}{r}}_0\left(\mathrm{\&lambda;}\right)={(R\cos \mathrm{\&lambda;},R\sin \mathrm{\&lambda;})}^T---\left(11\right)$

For current example, in order to describe the data on the detecting device, { u, w} are useful to introduce rotating coordinate system.Can suppose Initial point for rotating coordinate system.With reference to figure 7c, Fig. 7 c shows: and fixed coordinate system (x, y), its initial point is at the rotation center in source; { u, its initial point of w} are at the source point place, and the radius of track while scan is R for rotating coordinate system.Shown in Fig. 7 c,, can be written as along the vector of unit length of u axle and w axle for the rotation angle λ in the fixed coordinate system ${\hat{e}}_u\left(\mathrm{\&lambda;}\right)={(-\sin \mathrm{\&lambda;},\cos \mathrm{\&lambda;})}^T$ With ${\hat{e}}_w\left(\mathrm{\&lambda;}\right)={(\cos \mathrm{\&lambda;},\sin \mathrm{\&lambda;})}^T.$ And, regional Ω _RIn point stationary coordinate (x, y) and rotational coordinates u, the pass of w} is:

x＝-usinλ+(w+R)cosλ(12)

y＝ucosλ+(w+R)sinλ(13)

Be without loss of generality, consider the linear pattern detecting device, it is parallel to all the time

And the distance apart from the source is S, the coordinate u of any on the detecting device _dCan be expressed as:

u _d＝-(S/w)u(14)

Look back the example of the general track shown in Fig. 5 a and the 5b, can suppose that track satisfies two conditions: (1) ρ (s)＞ρ _sOr R (s)＞R _s(2) Be continuous, and be that segmentation (single order) can be little for arc length s.Condition (1) is meant that track can not intersect with support cylinder (or being equal to ground, image support).And, use path to come parametrization source track, along source track differentiate the time, avoided the coordinate singular point.Condition (2) has generality very much, and it can be satisfied by very various track, comprises the track of those potentially usefuls in imaging (such as the CT imaging applications of reality).An example of the track of satisfy condition (2) has been shown among Fig. 5 b.

As discussed above, many tracks can be suitable for imaging.The following a series of possible source track that comprises general helical trajectory of having described:

${\stackrel{\&RightArrow;}{r}}_0\left(s\left[\mathrm{\&lambda;}\right]\right)=(R\left(\mathrm{\&lambda;}\right)\cos \mathrm{\&lambda;},R\left(\mathrm{\&lambda;}\right)\sin \mathrm{\&lambda;},Z\left(\mathrm{\&lambda;}\right)),---\left(15\right)$

Wherein, λ represents rotation angle, and path s (λ) with the pass of rotation angle λ is:

$s\left(\mathrm{\&lambda;}\right)={\&Integral;}_0^{\mathrm{\&lambda;}}\left|\frac{d{\stackrel{\&RightArrow;}{r}}_0\left({\mathrm{\&lambda;}}^{\&prime;}\right)}{d{\mathrm{\&lambda;}}^{\&prime;}}\right|d{\mathrm{\&lambda;}}^{\&prime;}---\left(16\right)$

Utilize this parametrization to express, helical trajectory has radius variable R (λ) and variable pitch

As long as $\frac{d{\stackrel{\&RightArrow;}{r}}_0\left(s\right)}{\mathrm{ds}}(=\frac{d{\stackrel{\&RightArrow;}{r}}_0\left(s\left[\mathrm{\&lambda;}\right]\right)}{\mathrm{d\&lambda;}}\frac{\mathrm{d\&lambda;}}{\mathrm{ds}})$ Almost everywhere exists, and string method for reconstructing discussed below just can be applied to according to the data that obtain with this track based on the string reconstructed image.As R (λ)=R ₀And $Z\left(\mathrm{\&lambda;}\right)=\frac{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">h</figure-callout>}}{2\mathrm{\&pi;}}\mathrm{\&lambda;}$ The time,

Formula represent conventional helical trajectory, this track has constant radius R ₀With constant pitch h.In addition, saddle rail and tilting screw track all satisfy this general helix parameter expression.Particularly, saddle rail can be determined by following formula:

${\stackrel{\&RightArrow;}{r}}_0\left(s\left[\mathrm{\&lambda;}\right]\right)=({\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0\cos \mathrm{\&lambda;},{\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0\sin \mathrm{\&lambda;},\mathrm{<figure-callout\; id="2"\; label="h\; cos"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">h</figure-callout>}\cos 2\mathrm{\&lambda;})---\left(17\right)$

The tilting screw track can be expressed as:

${\stackrel{\&RightArrow;}{r}}_0\left(s\left[\mathrm{\&lambda;}\right]\right)=({\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0\cos \mathrm{\&lambda;},{\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0\sin \mathrm{\&lambda;},\cos \mathrm{\&mu;},{\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0\sin \mathrm{\&lambda;}\sin \mathrm{\&mu;}+\frac{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">h</figure-callout>}}{2\mathrm{\&pi;}}\mathrm{\&lambda;})---\left(18\right)$

Wherein, μ is a constant, the actual turning axle of expression inclination CT support (gantry) and the angle between the z axle.For saddle rail and tilting screw track,

All exist.Therefore, method for reconstructing can be applicable to, and according to the data of obtaining with these tracks, comes reconstructed image based on string.

With reference to figure 8a-c, rebuild at string discussed below, but show the example of different energy tracks.Fig. 8 a shows general helical trajectory, and Fig. 8 b shows circular arc-straight path, and Fig. 8 c shows circular arc-arc track.Track among Fig. 8 b and the 8c only is a piecewise differential.The string method for reconstructing that will go through below can support wherein to have the track of limited bending.Particularly, these tracks are such tracks, wherein, and limited isolated point place on track, Do not exist.In order to obtain the image on the string (thick line), orbit segment (bold curve shown in the figure) can be passed in the source.

Circle-straight path can be expressed as follows at path:

${\stackrel{\&RightArrow;}{r}}_0\left(s\right)=\left\{\begin{array}{cc}(0,s\sin \left(\mathrm{\&alpha;}\right),s\cos \left(\mathrm{\&alpha;}\right))& s\&le;0\\ {\mathrm{\&rho;}}_d(\cos \frac{s}{{\mathrm{\&rho;}}_d}-1,\sin \frac{s}{{\mathrm{\&rho;}}_d},0)& 0<s<{2\mathrm{\&pi;\&rho;}}_d\\ (0,(s-{2\mathrm{\&pi;\&rho;}}_d)\sin \left(\mathrm{\&alpha;}\right),(s-{2\mathrm{\&pi;\&rho;}}_d)\cos \left(\mathrm{\&alpha;}\right))& {2\mathrm{\&pi;\&rho;}}_d<s\end{array}\right\}---\left(19\right)$

Wherein, ρ _dThe radius that can represent circular arc, the angle of cut of straight line and the vertical line in the y-z plane is the α radian.Similarly, circular arc-arc track can be expressed as:

${\stackrel{\&RightArrow;}{r}}_0\left(s\right)=\left\{\begin{array}{cc}{\mathrm{\&rho;}}_{\mathrm{cc}}(\cos \frac{s}{{\mathrm{\&rho;}}_{\mathrm{cc}}},\sin \frac{s}{{\mathrm{\&rho;}}_{\mathrm{cc}}},0)& -{2\mathrm{\&pi;\&rho;}}_{\mathrm{cc}}<s<0\\ {\mathrm{\&rho;}}_{\mathrm{cc}}(\cos \frac{s}{{\mathrm{\&rho;}}_{\mathrm{cc}}},\sin \left(\mathrm{\&alpha;}\right)\sin \frac{s}{{\mathrm{\&rho;}}_{\mathrm{cc}}},\cos \left(\mathrm{\&alpha;}\right)\sin \frac{s}{{\mathrm{\&rho;}}_{\mathrm{cc}}})& 0\&le;s<{2\mathrm{\&pi;\&rho;}}_{\mathrm{cc}}\end{array}\right\}---\left(20\right)$

ρ wherein _CcThe radius of expression circular arc.In each case, when the source was scanned according to corresponding orbit segment, shown string can be rebuild.And, may there be the end points that connects string more than one path, in this case, every paths can be used for rebuilding this string.For the circular arc-straight path shown in Fig. 8 b, in the junction of straight line and circular arc, do not exist, but as long as track at this point continuously, just can be used string method for reconstructing discussed below about the derivative of path.There is same situation in circular arc-arc track for shown in Fig. 8 c in the junction of two circular arcs.

In the process that data are obtained, the source is adjusted

As previously discussed, even only need a fraction of image of object, common imaging system also need to obtain object whole cross section data and need handle all data of obtaining.In one aspect of the invention, if ROI is the part of object support, such as being the part in contiguous cross section or the part of volume, then can select at least one characteristic in source, this characteristic is obtained the data of the data of whole object support imaging being lacked than being enough to, but obtains the data that are enough at least the ROI imaging.For example, described at least one characteristic in source is controlled the supporting section that can make it possible to shine filling ROI.

As discussed earlier, source 312 comprises any device that can produce the signal (or combination of signal) that can be received by detecting device 320.The controllable characteristics in source comprises any aspect of the signal that influencing of source receive by detecting device, and these aspects include, but is not limited to: range of exposures (aperture as bundle is set, the width of bundle, the change of cone-beam scope etc.), the intensity of bundle and the spectrum of bundle distribute.Typically, the characteristic in source (such as range of exposures) is maintained fixed in imaging process.

In another aspect of this invention, can adjust at least one characteristic in source, so that the data that produce are lacked than the data that are enough to the object support imaging.Characteristic can be adjusted into it can be remained unchanged when the relative object of which movement in source.Perhaps, when the relative object of which movement in source, can adjust characteristic once at least.In one embodiment, one or more characteristics in source can be adjusted according to ROI.For example, the adjustable features in source can comprise the range of exposures in source.Particularly, the range of exposures in source can be adjusted into and make this scope point to ROI substantially, and non-ROI is significantly reduced (perhaps not pointing to non-ROI substantially).Like this, the source can reduce or minimize the irradiation of non-ROI, and the source is enough to object image-forming (such as by producing supporting section) the irradiation of ROI.When the irradiation of hope reduction or restriction source (such as x-ray source), this has superiority.To the feasible irradiation that can reduce of the adjustment of range of exposures, still keep range of exposures simultaneously to ROI area or volume to non-ROI area or volume.

Common situation is that range of exposures can be adjusted based on the type in the source of using in the imaging system.If the source produces fan-beam, the aperture that then can adjust the source is provided with the angle that changes fan-beam, will go through below.If the source produces collimated beam, then can adjust the width of light beam.If the source produces cone-beam, then can adjust the spread of cone-beam.

And the adjustment of one or more characteristics in source can be dynamic, in the source during with respect to object of which movement the characteristic in (for example, the source mobile object is static, the source stationary object moves or source and object move relative to each other) source on one point or the multiple spot place change.For example, the initial range of exposures in source can be elected as, make the initial directed towards object in this source.Initial range of exposures can be elected as, make the irradiation of non-ROI area is reduced or minimizes.When the relative object of which movement in source, the characteristic in source (for example range of exposures) can be adjusted.The point place that adjustment can be dispersed on track carries out.Perhaps, can adjust, so that this characteristic remains unchanged when the relative object of which movement in source.

Be the example of during the CT image scanning, adjusting the characteristic in source below.Fan-beam scanning is widely used in the Clinical CT system that is used for obtaining data.Yet the CT system can use the scanning of other type.Only as an example, cone-beam scan (for example helical cone-beam scanning) also can be used in the CT system.In fan-beam scanning, when fan-beam scanning covers 2 π or π and adds the angular range at fan-beam angle, be referred to as to scan fully (full-scan) or short scanning (short-scan) respectively.Angular range is called as simplification scanning (reduced scan) than the also little fan-beam scanning of short scanning.

In practice, the fan-beam geometric configuration with arc track is the most widely used structure.Yet, can use other structure.In this structure, field of view (FOV) is to be determined by the radius R of the subtended angle of fan-beam and track.Because some does not allow data truncation to the method for reconstructing (such as filtered back projection to be discussed below (FBP) method) that ROI rebuilds at any scanning visual angle, so the support of entire image must be in FOV.Provide two kinds of situations below, wherein, data truncation when obtaining, data has taken place, and the image of the image rebuilding method (such as backprojection-filtration to be discussed below (BPF) method) that demonstrates other in can accurate reconstruction ROI under the both of these case that data truncation has taken place.Suppose that scanning is included in angular range λ _MinAnd λ _MaxOn suitable track.As discussed earlier, suitable track can comprise such track, wherein, and by one group of string section of track definition of filling ROI.Also suppose, at each visual angle λ ∈ [λ _Min, λ _Max], and only can obtain data in the drop shadow spread in the support portion, will go through below.

Under first kind of situation, the subtended angle of fan-beam remains unchanged, and therefore FOV remains unchanged, but under second kind of situation, the different visual angle place of the subtended angle of fan-beam in the scanning angle scope can change.As shown below, two kinds of situations produce enough data, to satisfy [the λ at λ ∈ _Min, λ _Max] time, and only can obtain data in the drop shadow spread in the support portion.Under first kind of situation, the subtended angle of locating fan-beam at the scanning visual angle remains unchanged.Because fan-beam has fixing subtended angle, so can obtain all the time at [u _Dm, u _Dm] on data, here ± u _DmThe point of representing outermost two rays of fan-beam and detector array to intersect.Suppose that ROI is covered by FOV fully, and have one group of PI line that this group PI line is filled ROI and do not intersected with the support of ROI outside.Under this hypothesis, can see that for all support portions on the PI line in the ROI, their drop shadow spreads on detecting device satisfy [u _D1, u _D2]  [u _Dm, u _Dm].Therefore, for each support portion, [u _D1, u _D2] in data can obtain, so just produced enough data.Even image support also can obtain at [u all the time than FOV big (show to measure to contain and block) _Dm, u _Dm] interior data, and thereby can obtain at [u all the time _D1, u _D2] interior data.Therefore, the image on the PI line segment can be with fan-beam BPF method according to containing the data accurate reconstruction of blocking.Because can rebuild, therefore can obtain the image in the ROI at each selected PI line segment of filling ROI.Two examples of the track that to be illustration below enough and the data of q.s.

Referring to Fig. 9 a-c, at [λ _Min, λ _Max] in show fan-beam scanning, wherein the subtended angle of fan-beam remains unchanged, FOV is surrounded by the circle of solid line.At [λ _Min, λ _Max] on track while scan with black curve indication, solid line circle and dashed curve area surrounded are represented FOV and image support respectively.The ROI that is considered describes with the shadow region, by x _{π 1}With x _{π 2}Between the thick line section shown in support portion [x _{π 1}, x _{π 2}] represented the intersection between image support and the PI line segment, this PI line segment is by λ ₁And λ ₂, definite and crossing with image support.Fig. 9 a.c is with three visual angle λ ∈ [λ ₁, λ ₂] shown that (it is [u on the detecting device in the drop shadow spread on the detecting device in the support portion _D1, u _D2] between the thick line section).± u _mThe point of representing outermost two rays of fan-beam and detecting device to intersect, subtended angle by the source that connects λ place respectively and-u _mAnd u _mTwo lines form.

Shown in Fig. 9 a-c, the entire image of being represented by dashed curve supports bigger than FOV.Therefore, at most of visual angle λ ∈ [λ _Min, λ _Max] data for projection that obtains will contain and block.Consider the image reconstruction in the ROI shown in the shadow region (this ROI is limited in the FOV).Can select one group of PI line segment, each PI line segment is by λ ₁And λ ₂Determine, wherein λ ₁=λ _MinAnd λ ₂=∈ [λ _Min, λ _Max].Therefore, ROI can be by these PI line segment complete filling, and thereby are suitable tracks.Particularly, for the group in by λ ₁, λ ₂The PI line segment of determining is in order to carry out image reconstruction, [λ on this PI line segment ₁, λ ₂]  [λ _Min, λ _Max], therefore, this scanning angle scope is suitable.

Shown it is among Fig. 9 a-c by λ ₁, λ ₂The support portion of the PI line segment of determining and at three different visual angles λ ∈ [λ ₁, λ ₂] drop shadow spread.As can be seen, although containing, the projection of entire image at these visual angles block, at [u _Dm, u _Dm] data of go up gathering contain [u _D1, u _D2] necessary data in (that is, the drop shadow spread of support portion), this is because [u _D1, u _D2]  [u _Dm, u _Dm].This means and to utilize fan-beam BPF side to rebuild exact image based on support portion (perhaps, being equal to ground) based on its PI line segment.Top analysis also can be applied to all PI line segments of complete filling ROI.Therefore, can utilize the image on these PI line segments of fan-beam BPF algorithm accurate reconstruction, as a result accurate reconstruction the image among the ROI.

Under second kind of situation, the subtended angle of fan-beam can change at different visual angles.As discussed above, when source during with respect to object of which movement, the characteristic in source (such as the subtended angle of fan-beam) can be adjusted.Suppose support portion on selected PI line segment in ROI, and the subtended angle of fan-beam changes in the following manner: at each visual angle, fan-beam only contains the ray that (or containing substantially) and ROI intersect.This hypothesis make and only in the drop shadow spread in the support portion of the PI of complete filling ROI line segment (that is, and only at [u _D1, u _D2] in) can collect data.Therefore, even the data of gathering have serious blocking like this, but they contain the necessary data of support accurate reconstruction.Therefore, can come image on the accurate reconstruction PI line segment according to these data by utilizing fan-beam BPF method.

With reference to Figure 10 a-c, similar with Fig. 9 a-c, the data that show fan-beam scanning are obtained.Identical among mark and symbol and Fig. 9 a-c, just the subtended angle of fan-beam is at different visual angle λ ∈ [λ ₁, λ ₂] can change.Particularly, this subtended angle now by with the source at λ place respectively with u _D1And u _D2Two lines that connect form.Initial FOV and fan-beam are represented with dashed curve.Illustrated among Figure 10 a-c at three different visual angle λ ∈ [λ ₁, λ ₂, by [λ ₁, λ ₂] the drop shadow spread of support portion on the PI line segment determined.Subtended angle at three different places, visual angle: (1) is littler than the subtended angle that covers FOV; (2) significantly different with three subtended angles shown in Fig. 9 a-c; (3) cover the support portion fully.For example, the subtended angle among Figure 10 c is zero, because on this visual angle, only needs a ray to cover support portion on this PI line segment.As a result, can be at u ' _d∈ [u _D1, u _D2] (that is, in the drop shadow spread of the support portion of PI line segment) image data.Therefore, even such as having limited the output in source, still can gather enough data with by utilizing fan-beam BPF method to rebuild exact image on the PI line segment by fan-beam is narrowed down.And top analysis is applicable to all the PI line segments in selected group of the PI line segment that covers ROI.Therefore, by the image of fan-beam BPF algorithm on can these PI line segments of accurate reconstruction, as a result accurate reconstruction the image among the ROI.The subtended angle of the variation among Figure 10 a-c shows at single support portion.When considering whole ROI (that is, shadow region among Figure 10 a-c), can change subtended angle, so that at all visual angle λ ∈ [λ ₁, λ ₂], fan-beam only covers this ROI.

Be Computer Simulation research below, be used to demonstrate the fan-beam BPF method that is proposed with quantitative verification.In numeral research, consider circular arc fan-beam structure, wherein, orbital radius is R=27.0cm, and (virtual) one dimension (1-D) detector array is listed in the rotation center place.In the case, S=R=27.0cm.The square part that this one-dimensional detector array is 0.55mm by 512 each length of sides is formed.Like this, when the subtended angle of fan-beam remained unchanged to all projection visual angles, the fan-beam structure was held the FOV that radius is 12.5cm.Use two-dimentional head model, it has oval the support, and this ellipse supports along the semiaxis length of x axle and y axle and is respectively 9.6cm and 12.0cm.Consider two kinds of track while scans, shown in Figure 11 a and 11b.Particularly, Figure 11 a covers the angular range of [π, 2 π] and Figure 11 b covers the angular range of [1.2 π, 1.8 π].Shadow region among Figure 11 a-b is ROI to be rebuild.And shown in Figure 11 a-b, one group of PI line segment of assembling is used to fill ROI.Each PI line segment in this group is by λ ₁, λ ₂Determine, wherein, λ ₁=λ _Min, λ ₂∈ [λ _Min, λ _Max].

For the track while scan among Figure 11 a, use previously described have fixedly the fan-beam structure and the head model of subtended angle, data produce at 512 projection visual angles that are evenly distributed on [π, 2 π], shown in Figure 12 a.In this case, suppose not contain and block in each perspective data.Do not block because data do not contain, can use based on the method for FBP and rebuild exact image in the ROI based on the PI line segment that intersects with ROI.The image of rebuilding is presented among Figure 12 b, and wherein, every horizontal line is all represented a PI line segment.Use PI line coordinates (x discussed above _π, λ ₁, λ ₂) (image that provides with the PI line coordinates among Figure 12 b can convert the image that provides with stationary coordinate shown in Figure 12 c to for x, the y) relation between with stationary coordinate.In order to show that algorithm based on FBP is a response data noise how, adds Gaussian noise in the noise free data that is produced to.The standard deviation of Gaussian noise is fan-beam data peaked 2%.Based on noisy data, shown " noise is arranged " image in the ROI that rebuilds among Figure 12 d.Utilize fan-beam BPF method, can also reconstruct the image of similar Figure 12 c and 12d according to data presented among Figure 12 a.And, use fan-beam BPF method, the information that the data among Figure 12 a the contain information more required than the exact image of reconstruction ROI is many.

For the track while scan among Figure 11 a, use previously described fan-beam structure and the head model that changes subtended angle that have, produce data at 512 projection visual angles that are evenly distributed on [π, 2 π], shown in Figure 13 a.Subtended angle changes, make for the scanning visual angle, and only at u ' _d∈ [u _D1, u _D2] obtain data (that is the drop shadow spread of support portion on the PI line segment).Therefore, these group data are enough to reconstructed image.The comparison of Figure 13 a and 13b can demonstrate, and the data of obtaining with the subtended angle that changes contain blocks.Therefore, the image in the data accurate reconstruction ROI that can not block according to this group based on the algorithm of FBP.Yet, as previously mentioned, use fan-beam BPF method or MFBP method, can accurately rebuild the PI line segment that intersects with ROI (or accurate substantially).Figure 13 b has shown the image of rebuilding based on the PI line segment.The PI line coordinates has been carried out normalization at the length of each PI line segment.Use relation between PI line coordinates and the stationary coordinate (discussing in more detail below) again, the image transitions that provides with the PI line coordinates among Figure 13 b is become the image that provides with stationary coordinate shown in Figure 13 c.Fan-beam BPF algorithm also is used for coming reconstructed image according to the data that contain Gaussian noise, and the noise image that has of reconstruction is presented among Figure 13 d.

For the track while scan among Figure 11 b, use above-described fan-beam structure and head model with flare angle variation, produce data by 416 projection visual angles on being evenly distributed on shown in Figure 14 a [1.09 π, 1.91 π].And, change subtended angle, make visual angle for scanning, and if only if u ' _d∈ [u _D1, u _D2] (that is, the support portion is in the drop shadow spread on the PI line segment) just obtain data.Therefore, these group data are enough for reconstructed image.To showing of Figure 12 a and 14a more clearlyly, these group data contain serious blocking.In fact, all contain in the data of all scannings under visual angles on [1.09 π, 1.91 π] and block.For some visual angle, as near λ _MinThe visual angle of=1.09 π, only the end in detector array blocks.Yet, for remaining scanning visual angle, all data truncation can take place at the two ends of detector array.Can not there be the data of seriously blocking to come in ROI accurately reconstructed image according to this group based on the method for FBP.Yet, as mentioned above, can use fan-beam BPF method or MFBP method, rebuild the exact image on the PI line segment that intersects with ROI.Fig. 1 4b has showed the reconstructed image on these PI line segments.Based on the relation between PI line coordinates discussed below and the stationary coordinate, can become the image transitions among Figure 14 b the image among Figure 14 c, the image among Figure 14 c shows by stationary coordinate.Fan-beam BPF algorithm also is used for according to the data reconstructed image that contains Gaussian noise, and the noise image of reconstruction is presented among Figure 14 d.

In data acquisition, adjust detecting device

As previously mentioned, detecting device 320 can comprise any device of detection signal (or combination of signal).Signal can be from the source 312, perhaps can be from object 316.In another aspect of this invention,, can revise at least one characteristic of detecting device obtaining imaging with in the process of data.In one embodiment, can revise the characteristic of detecting device according to ROI.For example, the characteristic that is modified of detecting device can comprise the activation or the inactivation of the each several part of detecting device.322 parts of detecting device 320 can be enabled or forbid, and make data that detecting device 320 detects roughly at ROI and roughly not at non-ROI.Like this, can reduce or minimize irrelevant data.In another embodiment, can be based on the data that ROI accepts or the refusal detecting device produces.Can accept or refuse the data that 322 parts of detecting device 320 produce, make data that detecting device 320 detects roughly at ROI and roughly not at non-ROI.Like this, can reduce or minimize irrelevant data.Detecting device 320 can determine whether to accept or refuse the data from a part.Alternatively, processing unit 304 can determine whether to accept or refuse the data from a part.

Generate image based on string

After data are obtained, can deal with data to generate part or all reconstructed image of object.Reconstruction can be based at least a portion of filling area-of-interest (ROI) string of (as all).At the string that rebuild to use can be line between 2, as the part of straight line or curve.

String can be based on any aspect of imaging, as the on-fixed coordinate system.Such on-fixed coordinate system can be limited by the source track at least in part, perhaps according to the source with respect to object how to move (for example, source movement and object is static, the perhaps static and object of which movement in source, perhaps source and object relative to each other move) limit.After reconstructed image on the on-fixed coordinate system, can be in fixed coordinate system (as Cartesian coordinates) this image transformation.Alternatively, string can be based on fixed coordinate system, as Cartesian coordinates.

For example, image reconstruction can be to the string of small part based on the qualification of source track.As previously mentioned, 2 on the track of source can limit a string.Point on the string can also be by thirdly limiting.Like this, can utilize being different from first second point and being formed on the string between described first and described second thirdly on the point of first on the source path, the source path, limit string.First and second can limit with scalar, perhaps can limit with the arc length on the source path.No matter whole ROI is the ROI or the three-dimensional ROI of two dimension, and the point on the string that can be limited by the source track limits.And, can use string to come reconstructed image.Only as an example (below go through), reconstructed image in the following manner: discern one group of right string of point that connects on the source path, wherein, this group string has been filled the volume of the area-of-interest in the main body; According to the image density on the data computation string of gathering; And based on this image density and source path structure 3-D view.Therefore, when using the reconstruction that limits by the source track to use string, can be based on the coordinate system reconstructed image of source track qualification.

For example, as mentioned above, Fig. 4 a and 4b define at the point on the string in whole ROI zone.As another example, Figure 15 a-c has shown a columnar object that is just being scanned by helical source trajectory.The shape of object and the type of track only are exemplary.Also can scan other object, and can use other track.Every bit in the object can limit by the point on the string.For example, the string that the source track among Figure 15 a-c limits can be filled the whole volume of columnar object by limiting the face of a series of filling objects.Shown three faces among Figure 15 a-c, and corresponding reconstructed image.

Owing to can limit ROI by at least a portion string, so can utilize string to come reconstructed image.Particularly, can be at least a portion of string reconstructed image to produce image at ROI.In the example that Fig. 4 a and 4b show, can be on the section that overlaps with ROI of string reconstructed image, perhaps can be on whole string reconstructed image.In the example that Figure 15 a-c shows, can be on the surf zone of the volume that constitutes ROI the design of graphics picture, perhaps can be on the whole surf zone that string limits the design of graphics picture.Alternatively, the volume that can the pointwise construct image constitutes ROI.Can make and in all sorts of ways based on the string reconstructed image.In the example below, describe the method for three kinds of reconstructed images, comprised filtered back projection (FBP), backprojection-filtration (BPF) and minimum filtered back projection (MFBP).But, also can use other method.And described example has been used cone beam projection.Also can use other projection, comprise fan-beam projection.Perhaps, may not need projection, as the PET scan condition.

The cone beam projection function or the Density Distribution of object can be defined as:

$D({\stackrel{\&RightArrow;}{r}}_0\left(s\right),\widehat{\mathrm{\&beta;}})={\&Integral;}_0^{\&infin;}\mathrm{dtf}({\stackrel{\&RightArrow;}{r}}_0\left(s\right)+t\widehat{\mathrm{\&beta;}}),---\left(21\right)$

Vector of unit length wherein

Expression is through point

The projecting direction of an X ray, can be written as:

$\widehat{\mathrm{\&beta;}}=\frac{{\stackrel{\&RightArrow;}{r}}^{\&prime;}-{\stackrel{\&RightArrow;}{r}}_0\left(s\right)}{|{\stackrel{\&RightArrow;}{r}}^{\&prime;}-{\stackrel{\&RightArrow;}{r}}_0\left(s\right)|},---\left(22\right)$

And $\stackrel{\&RightArrow;\&prime;}{r}\&Element;R^3.$ Can be called physical data, because they are considered to measurable.Suppose

By s _aAnd s _bOn the string that (2 points on the track of source) limit.For the broad sense track, suppose s ∈ [s _a, s _b] N-1 bending arranged on the orbit segment of appointment, orbit segment is divided into N continuous segment.N-1 bending can be designated as s ₁(i ∈ [2, N]), and s ₁=s _a, s _N+1=s _bFor on the string of a musical instrument The object function

Can be by accurate reconstruction:

$f\left(\stackrel{\&RightArrow;}{r}\right)={\&Integral;}_{R^3}d\stackrel{\&RightArrow;\&prime;}{r}K(\stackrel{\&RightArrow;}{r},\stackrel{\&RightArrow;\&prime;}{r})g\left(\stackrel{\&RightArrow;\&prime;}{r}\right),---\left(23\right)$

Wherein, the integral kernel in the following formula

Can be expressed as:

$K(\stackrel{\&RightArrow;}{r},\stackrel{\&RightArrow;\&prime;}{r})=\frac{1}{2\mathrm{\&pi;j}}{\&Integral;}_{R^3}d\stackrel{\&RightArrow;}{v}\mathrm{sgn}[\stackrel{\&RightArrow;}{v}\&CenterDot;\widehat{e_c}]{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">e</figure-callout>}}^{2\mathrm{\&pi;j}\stackrel{-}{v}\&CenterDot;(\stackrel{\&RightArrow;}{r}-\stackrel{\&RightArrow;\&prime;}{r})}---\left(24\right)$

Broad sense back projection

Can be expressed as:

$g\left({\stackrel{\&RightArrow;}{r}}^{\&prime;}\right)={\&Integral;}_{s_a}^{s_b}\frac{\mathrm{ds}}{|{\stackrel{\&RightArrow;}{r}}^{\&prime;}-{\stackrel{\&RightArrow;}{r}}_0\left(s\right)|}\frac{\&PartialD;}{\&PartialD;q}\stackrel{-}{D}({\stackrel{\&RightArrow;}{r}}_0\left(q\right),\widehat{\mathrm{\&beta;}}){|}_{q=s}---\left(25\right)$

$=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\&Integral;}_{s_i}^{s_{i+1}}\frac{\mathrm{ds}}{|\stackrel{\&RightArrow;\&prime;}{r}-{\stackrel{\&RightArrow;}{r}}_0\left(s\right)|}\frac{\&PartialD;}{\&PartialD;q}\stackrel{-}{D}({\stackrel{\&RightArrow;}{r}}_0\left(q\right),\widehat{\mathrm{\&beta;}}){|}_{q=s}$

And the expanded data function can be defined as:

$\stackrel{-}{D}({\stackrel{\&RightArrow;}{r}}_0\left(s\right),\widehat{\mathrm{\&beta;}})=D({\stackrel{\&RightArrow;}{r}}_0\left(s\right),\widehat{\mathrm{\&beta;}})-D({\stackrel{\&RightArrow;}{r}}_0\left(s\right),-\widehat{\mathrm{\&beta;}})---\left(26\right)$

As mentioned above, can realize utilizing the image reconstruction of string by multitude of different ways.As shown below, can come accurate reconstruction object function based on filtered back projection (FBP), backprojection-filtration (BPF) and minimum filtered back projection (MFBP) Also can use other method to come based on the string reconstructed image.

The explicit form of reconstruction algorithm may depend on the selection to coordinate system usually.For the every bit s on the track, with { w} represents rotating coordinate system for u, v.The initial point of supposing it exists

The place, and its vector of unit length can be expressed as:

${\hat{e}}_u\left(s\right)=(-\sin \left(s\right),\cos \left(s\right),0),{\hat{e}}_v\left(s\right)=\left(\mathrm{0,0,1}\right),{\hat{e}}_w\left(s\right)=(\cos \left(s\right),\sin \left(s\right),0)---\left(27\right)$

Make (x, y, z) and (w) expression is positioned at the coordinate of the point of support column at fixed coordinate system and rotating coordinate system respectively for u, v, and then they can show and satisfy following the relation:

x＝-usin(s)+wcos(s)+x ₀(s)

y＝ucos(s)+wsin(s)+y ₀(s)(28)

z＝v+z ₀(s)

As can be seen, u-w face in the rotating coordinate system and v axle are parallel to x-y face and the z axle in the fixed coordinate system respectively.

Can use two dimension (2D) detecting device, its normal vector is

Point on the track

Distance be S (s)＞0.On the detecting device face, can use { u _d, v _dRepresent 2D coordinate system { u, the cone beam projection of v}.Like this, axle u _dAnd v _dRespectively along

With

And { the u of detector coordinates system _d, v _dInitial point be positioned at

Projection place on the detecting device face.Now, the arbitrfary point on the detecting device face can be fully according to (u _d, v _d) represent.Can easily draw:

$u=-\frac{w}{S\left(s\right)}{u}_d,$ With $v=-\frac{w}{S\left(s\right)}{v}_d---\left(29\right)$

With regard to CT scan, because from

Independent x ray in the cone-beam of the source point at place fully can be by detector coordinates u _dAnd v _dRepresent, so can also use P (u _d, v _d, s) represent data

$P(u_d,v_d,s)=D({\stackrel{\&RightArrow;}{r}}_0\left(s\right),\widehat{\mathrm{\&beta;}}),$ With $\frac{\&PartialD;}{\&PartialD;q}D({\stackrel{\&RightArrow;}{r}}_0\left(q\right),\widehat{\mathrm{\&beta;}}){|}_{q=s}=\frac{\mathrm{dP}(u_d,v_d,s)}{\mathrm{ds}}{|}_{\widehat{\mathrm{\&beta;}}}---\left(30\right)$

Wherein,

Also satisfy:

$\widehat{\mathrm{\&beta;}}\frac{1}{A(u_d,v_b)}[u_d{\hat{e}}_u\left(s\right)+v_{d{\hat{e}}_v}\left(s\right)-S\left(s\right){\hat{e}}_w\left(s\right)]---\left(31\right)$

$A(u_d,v_d)=\sqrt{{\mathrm{<figure-callout\; id="2"\; label="u\; d"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">u</figure-callout>}}_d^{}+{\mathrm{<figure-callout\; id="2"\; label="v\; d"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">v</figure-callout>}}_d^{}+S^2\left(s\right)}---\left(32\right)$

A kind of existing image rebuilding method is called as filtered back projection (FBP).Method based on FBP is carried out the non-change filtering that moves to corrected data earlier, again the data through filtering is weighted back projection, comes reconstructed image thus.Utilize the FBP method below,, come reconstructed image on string by adopting the cone beam projection data of the string of a musical instrument on the detecting device face.

Utilize condition (1) (2) and the formula (23) discussed in the above, again in conjunction with formula (24)-(26), obtained the exact image function on the whole string of a musical instrument, thereby also obtained the exact image function on the string.Provided image below

Accurate expression,

$f_R\left(\stackrel{\&RightArrow;}{r}\right)={\&Integral;}_{R^3}d\stackrel{\&RightArrow;}{v}\mathrm{sgn}[\stackrel{\&RightArrow;}{v}\&CenterDot;{\hat{e}}_c]\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\&Integral;}_{s_i}^{s_{i+1}}\mathrm{ds}[\stackrel{\&RightArrow;}{v}\&CenterDot;\frac{d{\stackrel{\&RightArrow;}{r}}_0\left(s\right)}{\mathrm{ds}}]F\left(\stackrel{\&RightArrow;}{v}\right){\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">e</figure-callout>}}^{{2\mathrm{\&pi;j}\stackrel{\&RightArrow;}{v}\&CenterDot;}_{{\stackrel{-}{r}}_0}\left(s\right)}\mathrm{\&delta;}(\stackrel{\&RightArrow;}{v}\&CenterDot;\stackrel{\&RightArrow;}{r}-\stackrel{\&RightArrow;}{v}\&CenterDot;{\stackrel{\&RightArrow;}{r}}_0\left(s\right))---\left(33\right)$

Wherein, the δ function has implied condition $\stackrel{\&RightArrow;}{v}\&CenterDot;(\stackrel{\&RightArrow;}{r}-{\stackrel{\&RightArrow;}{r}}_0\left(s\right))=0,$ Wherein On the string of a musical instrument.In addition,

Can be defined as:

${\widehat{e_c}}^{\&prime;}=\frac{1}{a}\left[{\hat{e}}_{c}x(\hat{r}-{\stackrel{\&RightArrow;}{r}}_0\left(s\right))\right]x{\hat{e}}_w,$ With ${\stackrel{\&RightArrow;}{V}}_d={\hat{e}}_{w}x\left[\stackrel{\&RightArrow;}{v}x{\hat{e}}_w\right]---\left(34\right)$

Wherein $a=\left|\left[{\hat{e}}_{c}x(\stackrel{\&RightArrow;}{r}-{\stackrel{\&RightArrow;}{r}}_0\left(s\right))\right]x{\hat{e}}_w\right|$ It is normalized factor.Vector of unit length

The direction of the cone beam projection of the expression string of a musical instrument on the detecting device face.

For on the string of a musical instrument Can easily derive ${\hat{e}}_w\&CenterDot;(\stackrel{\&RightArrow;}{r}-{\stackrel{\&RightArrow;}{r}}_0\left(s\right))<0.$ Use this result and $\stackrel{\&RightArrow;}{v}\&CenterDot;(\stackrel{\&RightArrow;}{r}-{\stackrel{\&RightArrow;}{r}}_0\left(s\right))=0,$ Can obtain:

$\mathrm{sgn}[\stackrel{\&RightArrow;}{v}\&CenterDot;{\hat{e}}_c]=\mathrm{sgn}[{\stackrel{\&RightArrow;}{v}}_d\&CenterDot;{\widehat{e_c}}^{\&prime;}]=\mathrm{sgn}\left[{v_c}^{\&prime;}\right]---\left(35\right)$

Wherein, ${v^{\&prime;}}_c={\stackrel{\&RightArrow;}{v}}_d\&CenterDot;{{\hat{e}}^{\&prime;}}_c.$ Like this, the part of formula (24) can be rewritten as:

$K(\stackrel{\&RightArrow;}{r},\stackrel{\&RightArrow;\&prime;}{r})=\frac{1}{2\mathrm{\&pi;j}}\frac{S^2\left(s\right)}{{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">w</figure-callout>}}^2}{\&Integral;}_{R}d{v^{\&prime;}}_c\mathrm{sgn}\left[{v^{\&prime;}}_c\right]{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">e</figure-callout>}}^{2\mathrm{\&pi;j}(u_c-{u\&prime;}_c){v\&prime;}_c}\mathrm{\&delta;}(u_{\&perp;}-{u^{\&prime;}}_{\&perp;})\mathrm{\&delta;}(w-w^{\&prime;})---\left(36\right)$ U wherein _cAnd u ' _cThe coordinate of the cone beam projection of the expression string of a musical instrument on the detecting device face, u _⊥Axle is perpendicular to u _cAxle.For on the string of a musical instrument

u _⊥=0.Therefore, can write this part of formula:

$K(\stackrel{\&RightArrow;}{r},{\stackrel{\&RightArrow;}{r}}^{\&prime;})=\frac{1}{{2\mathrm{\&pi;}}^2}\frac{S^2\left(s\right)}{{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">w</figure-callout>}}^2}\frac{1}{u_c-{u^{\&prime;}}_c}\mathrm{\&delta;}\left({u^{\&prime;}}_{\&perp;}\right)\mathrm{\&delta;}(w-w^{\&prime;})$

Because δ (w-w ') function in the formula (37) is so have only first (to that is to say physical data in the growth data function in formula (26)

) to the image g of back projection _c(x _c, s _a, s _b) contribution arranged.Therefore, following derivation is only considered from the physical data item

Contribution.

Because $d{\stackrel{\&RightArrow;}{r}}^{\&prime;}=\frac{w^{{\&prime;}^2}}{S^2\left(a\right)}d{u^{\&prime;}}_{c}d{u^{\&prime;}}_{\&perp;}d{w}^{\&prime;},$ So in formula (26) and (37) substitution formula (23), exchange u ' then _cIntegration order with s obtains:

$f(x_c,s_a,s_b)=\frac{1}{{2\mathrm{\&pi;}}^2}{\&Integral;}_{s_o}^{s_b}\mathrm{ds}{\&Integral;}_R\frac{d{u^{\&prime;}}_c}{u_c-{u^{\&prime;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="A20058001234800741.png,A20058001234800881.png"\; state="\{\{state\}\}">c</figure-callout>}}}\frac{1}{|{\stackrel{\&RightArrow;}{r}}^{\&prime;}-\stackrel{\&RightArrow;}{{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">r</figure-callout>}}_0}\left(s\right){|}^2}\frac{\mathrm{dp}({u^{\&prime;}}_d,{v^{\&prime;}}_d,s)}{\mathrm{ds}}{|}_{\widehat{\mathrm{\&beta;}}}---\left(38\right)$

Formula (38) is called as filtered back projection (FBP) algorithm, because it carries out Hilbert (Hilbert) conversion of one dimension earlier (also promptly to u ' _cIntegration), again through the data back projection of filtering to string (also promptly to the integration of s).The data of must use when the image of rebuilding with the FBP algorithm on the string not blocking are because the filtering in the FBP algorithm need be known u ' _cData on the ∈ R.

Based on the backprojection-filtration reconstructed image

The method of another reconstructed image is backprojection-filtration (BPF) method.Be different from existing method based on FBP, the BPF method is by first back projection data (as weighted data), again back projection carried out filtering (becoming filtering as non-moving), and in ROI reconstructed image.In general, back projection relates to measurement data is transformed to image space from data space.When back projection, can further revise data.For example, can weight data, perhaps can be to the data differentiate.Yet revising data when back projection is not to need.

When back projection, can at first select, and then data are transformed to image space from data space measurement data.When using string to carry out back projection, can select the projected data of string section on detecting device in the ROI.As example, with reference to Fig. 2 a, if the string section (being expressed as line 208) in the ROI that is used to rebuild is the horizontal line (being expressed as line 210) of part 204 bottoms, then the projection of this section on detecting device is the data from point " C " to point " D ".These data in from " C " to " D " scope can back projection on described string section.Alternatively, if the string section than section 208 long (as section of section of comprising 208 and extra section 212), then the projection of this section on detecting device is exactly the data from point " E " to point " F ".These data in from " E " to " F " scope can back projection on described string section.Like this, with the corresponding data of any string section, perhaps corresponding data with whole string, can back projection on this section.After back projection, can carry out filtering to the back projection on the particular segment.The section that is used for using the BPF method to rebuild ROI can comprise supporting section.According to the type of the image that will rebuild, can use different filtering methods.For example, point-device if desired reconstruction, then filtering method example is to use Hilbert transform.As another example,, then can use other filtering method if do not need point-device reconstruction.

Many data capture methods can be used to produce the data at the BPF method.The BPF method can be directly according to containing the simplification scan-data that blocks or, coming accurate reconstruction image in given ROI according to the data of not blocking.For example, data capture method previously discussed (wherein, having revised at least one characteristic (as the range of exposures in source) in source) also can be used for producing the data at the BPF method.

Be an example of using the BPF method under based on the situation of string reconstructed image below.Yet the BPF method is not limited to use string to come reconstructed image, also reconstructed image prevailingly.For example, the BPF method can be used for not considering the tradition reconstruction of string.

For by s _aAnd s _bWhat (point on the track of source) was definite is tuned up, and considers the coordinate system { x of initial point at the mid point of string _c, y _c, z _c.In this coordinate system, x _cAxle overlaps with the string of a musical instrument, and its vector of unit length is

And y _cAxle and z _cAxle is perpendicular to x _cAxle.Therefore, by s _aAnd s _bAny point on the string of a musical instrument of determining can be expressed as (x _c, s _a, s _b), and can use f _c(x _c, s _a, s _b) and g _c(x _c, s _a, s _b) come the back projection on the presentation video function and the string of a musical instrument, they satisfy:

$f\left(\stackrel{\&RightArrow;}{r}\right)=f_c(x_c,s_a,s_b),$ $g\left(\stackrel{\&RightArrow;}{r}\right)=g_c(x_c,s_a,s_b)---\left(39\right)$

Wherein,

And x _cBe associated by formula (6).By s _aAnd s _bBack projection's image on the string of determining is by P (u _d, v _d, s) be expressed as:

$g_c(x_c,s_a,s_b,)={\&Integral;}_{s_a}^{s_b}\frac{\mathrm{sgn}(-\widehat{\mathrm{\&beta;}\&CenterDot;}{\hat{e}}_w)\mathrm{ds}}{|\stackrel{\&RightArrow;}{r}\left(x_c\right)-{\stackrel{\&RightArrow;}{r}}_0\left(s\right)|}\frac{\&PartialD;}{\&PartialD;s}P(u_d,v_d,s){|}_{\widehat{\mathrm{\&beta;}}}---\left(40\right)$

The symbol factor in the integration comes from the expansion of the data function in the formula (26).For on the string of a musical instrument

Nuclear in the formula (24)

Can be rewritten as:

$K=(\stackrel{\&RightArrow;}{r},{\stackrel{\&RightArrow;}{r}}^{\&prime;})\frac{1}{2\mathrm{\&pi;j}}{\&Integral;}_R{\mathrm{dv}}_c\mathrm{sgn}\left[v_c\right]{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">e</figure-callout>}}^{2\mathrm{\&pi;j}{v}_e(x_c-{x^{\&prime;}}_c)}\mathrm{\&delta;}\left({y^{\&prime;}}_c\right)\mathrm{\&delta;}\left({z^{\&prime;}}_c\right)=\frac{1}{{2\mathrm{\&pi;}}^2(x_c-{x^{\&prime;}}_c)}\mathrm{\&delta;}\left({y^{\&prime;}}_c\right)\mathrm{\&delta;}\left({z^{\&prime;}}_c\right)---\left(41\right)$

Wherein ${{\stackrel{\&RightArrow;}{r}}^{\&prime;}\&Element;R}^3,$ v _cExpression is at x _cSpatial frequency.Formula (34) is applied to formula (23) can be got:

$f_c(x_c,s_a,s_b)=\frac{1}{{2\mathrm{\&pi;}}^2}{\&Integral;}_R\frac{d{x^{\&prime;}}_c}{x_c-{x^{\&prime;}}_c}{g}_c({{x^{\&prime;}}_c,s}_a,s_b)---\left(42\right)$

Wherein, x _c∈ R.Therefore, the image f on the string of a musical instrument _c(x _c, s _a, s _b) be the image g of back projection _c(x ' _c, s _a, s _b) along the Hilbert transform of the string of a musical instrument.The result of formula (42) provides the method that is used for rebuilding according to the knowledge of the projected image on the whole string of a musical instrument image on the string.Will more go through below, be limited in condition on the string, can see that image on the string can be rebuild according to the knowledge of the projected image on the string only to obtain by using image support.

x _S1And x _S2, being expressed as the end points of the crossing line segment of string and support cylinder, this crossing line segment is called the supporting section of string.Be without loss of generality, suppose x _S1≤ x _S2Consider the condition (1) of relevant track, [x _S1, x _S2]  [l, l], that is to say that supporting section is all the time in string, as shown in figure 16.Particularly, Figure 16 has described object support and source track, illustration supporting section (x _c∈ [x _S1, x _S2]) and the section (x of back projection _c∈ [x _C1, x _C2]).In formula (42) both sides at x _cDo Hilbert transform, obtain:

$g_c(x_c,s_a,s_b)=2{\&Integral;}_R\frac{d{x^{\&prime;}}_c}{{x^{\&prime;}}_c-x_c}{f}_c({x^{\&prime;}}_c,s_a,s_b)=2{\&Integral;}_{x_{c1}}^{x_{c2}}\frac{d{x^{\&prime;}}_c}{{x^{\&prime;}}_c-x_c}{f}_c({x^{\&prime;}}_c,s_a,s_b)---\left(43\right)$

X wherein _c∈ R, parameter x _C1And x _C2Satisfy x respectively _C1∈ (∞, x _S1], x _C2∈ [x _S2, ∞).[x _C1, x _C2] be called as back projection's section.The last part of formula (43) is by observing for x _c [x _S1, x _S2] and make f _c(x _c, s _a, s _b)=0 is determined.

The result of formula (43) is illustrated in a Hilbert transform on the finite interval, and its inverse transformation can be write:

$f_c(x_c,s_a,s_b)=\frac{1}{{2\mathrm{\&pi;}}^2}\frac{1}{\sqrt{(x_{c2}-x_c)(x_c-x_{c1})}}$

$\&times;[{\&Integral;}_{x_{c1}}^{x_{c2}}\frac{d{x^{\&prime;}}_c}{{x^{\&prime;}}_c-x_c}\sqrt{(x_{c2}-{x^{\&prime;}}_c)({x^{\&prime;}}_c-x_{c1})g_c({x^{\&prime;}}_c,s_a,s_b)}+C]---\left(44\right)$

Wherein, x _c∈ [x _S1, x _S2], x _cWith

Between relation determine that by formula (6) and constant C is provided by following formula:

$C=2\mathrm{\&pi;}{\&Integral;}_{x_{c1}}^{x_{c2}}{f}_c(x_c,s_a,s_b){\mathrm{dx}}_c=2\mathrm{\&pi;D}({\stackrel{\&RightArrow;}{r}}_0\left(s_a\right),{\hat{e}}_c)---\left(45\right)$

Because second in the formula (44) only is the constant term that can easily directly obtain from data, so the required amount of calculation of reconstructed image is determined by first in the formula (44) required compilation workload on the string of a musical instrument.

By revising first form, formula (44) can be rewritten as:

$f_c(x_c,s_a,s_b)=\frac{1}{2\mathrm{\&pi;}}\frac{1}{\sqrt{(x_{c2}-x_c)(x_c-x_{c1})}}[{\&Integral;}_R\frac{d{x^{\&prime;}}_c}{x_c-{x^{\&prime;}}_c}\mathrm{g\&pi;}({x^{\&prime;}}_c,s_a,s_b)+2\mathrm{\&pi;D}({\stackrel{\&RightArrow;}{r}}_0\left(s_a\right),{\hat{e}}_c)]---\left(46\right)$

Wherein,

$g_{\mathrm{\&pi;}}({x^{\&prime;}}_c,s_a,s_b)={\mathrm{\&Pi;}}_c\left({x^{\&prime;}}_c\right)\sqrt{(x_{c2}-{x^{\&prime;}}_c)({x^{\&prime;}}_c-x_{c1})g_c({x^{\&prime;}}_c,s_a,s_b)}---\left(47\right)$

As x ' _c∈ [x _C1, x _C2] time, ∏ _c(x ' _c)=1; And as x ' _c [x _C1, x _C2] time, ∏ _c(x ' _c)=0.(it can not dominance represent x ' to be different from first (that is the Hilbert transform on the finite interval) in the formula (44) _cNon-moving on the axle becomes filtering), formula (46) dominance has been represented whole x ' _cNon-moving on the axle becomes filtering (that is Hilbert transform).Such variation has practical significance with regard to calculating, because Hilbert transform this moment can utilize the fast Fourier transform (FFT) technology to calculate efficiently.

By analyzing formula (47), can see, the image on the string can according on the string by x _c∈ [x _S1, x _S2] supporting section determined back projection's image knowledge and accurately obtain.This is for rebuilding accurate image and provide the foundation according to containing being projected in of transversely truncation under may situation on the string.Formula (47) is called as backprojection-filtration (BPF) algorithm, because its first back projection data through revising (that is, is obtaining g _c(x ' _c, s _a, s _b) time to the s integration), again back projection's image of weighting is done the one dimension Hilbert transform (that is, to x ' _cIntegration).

Generate image based on minimum filtered back projection

The method of another reconstructed image is minimum filtered back projection (MFBP) method.The MFBP method is fundamentally different with existing FBP method, because be similar to the BPF method, the MFBP method allows to rebuild according to minimum data.Particularly, the MFBP method can be directly according to containing the simplification scan-data accurate reconstruction image in given ROI that blocks.Data capture method previously discussed (wherein, having revised at least one characteristic (as the range of exposures in source) in source) can be used for producing the data at the MFBP method.The MFBP method also can be according to not containing the data accurate reconstruction image that blocks.

When using the MFBP method at string, can to based on section or string the projected data on detecting device carry out filtering.Can use arbitrary section or whole string of string.Utilize the example shown in Fig. 2 a, the projection of section 210 is corresponding to the data from point " C " to point " D " on the detecting device.Can carry out filtering to these data.Then, can be on section 210 filtered data back projection.As discussed earlier, the type of filtering may depend on the image that will obtain, and quite accurate if desired image then can use Hilbert transform, if perhaps do not need quite accurate image, then can use other method.Similarly, can the section of use 210 section in addition.For example, can use the section of section of comprising 210 and extra segment 212.The section that is used for using the MFBP method to rebuild ROI can comprise supporting section.

Be an example of in based on the situation of string reconstructed image, using the MFBP method below.But, the MFBP method is not limited to utilize the string reconstructed image, and it is reconstructed image prevailingly also.For example, the MFBP method also can be used for the outer tradition reconstruction of string situation.

Described in the above example BPF method, by the back projection along the string of a musical instrument is made one-dimensional filtering, and based on the string reconstructed image.Also can do one-dimensional data filtering before back projection is to the string on detecting device comes based on the string reconstructed image.The MFBP method that describes below can be at any general track based on the string reconstructed image.Therefore, following MFBP method can be applied to any illustrative trace in this discussion.

In wushu (26), (30) and (47) the substitution formulas (46), and change x ' _cIntegration order with s obtains:

$f_c(x_c,s_c,s_b)=\frac{1}{{2\mathrm{\&pi;}}^2}\frac{1}{\sqrt{(x_{c2}-x_c)(x_c-x_{c1})}}$

$\&times;[{\&Integral;}_{s_o}^{s_b}\mathrm{ds}{\&Integral;}_R\frac{d{x^{\&prime;}}_c}{x_c-{x^{\&prime;}}_c}\frac{\sqrt{(x_{c2}-{x^{\&prime;}}_c)({x^{\&prime;}}_c-x_{c1})}}{|{\stackrel{\&RightArrow;}{r}}^{\&prime;}-{\stackrel{\&RightArrow;}{r}}_D\left(s\right)|}\&CenterDot;\mathrm{sgn}[-\widehat{\mathrm{\&beta;}}\&CenterDot;{\hat{e}}_w]\frac{\mathrm{dp}({u^{\&prime;}}_d,{v^{\&prime;}d}_{,}s)}{\mathrm{ds}}{|}_{\widehat{\mathrm{\&beta;}}}+C]---\left(48\right)$

Wherein,

And x _cThrough type (6) is associated;

And x ' _cBetween relation can be by with in the formula (6)

And x _cUse respectively

And x ' _cReplace simply and obtain; And C can be provided by formula (45).

For given s ∈ [s _a, s _b], make u _cRepresent the x on the detecting device _c∈ [x _C1, x _C2] cone beam projection, then can obtain:

$u_c=\frac{w_2(x_c-x_{c1})}{w_1(x_{c2}-x_c)+w_2(x_c-x_{c1})}---\left(49\right)$

Wherein, ${\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="A20058001234800741.png,A20058001234800881.png"\; state="\{\{state\}\}">w</figure-callout>}}_1=-[{\stackrel{\&RightArrow;}{r}}_0\left(s_a\right)-{\stackrel{\&RightArrow;}{r}}_0\left(s_a\right)]\&CenterDot;{\hat{e}}_w,$ And ${\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">w</figure-callout>}}_2=-[{\stackrel{\&RightArrow;}{r}}_0\left(s_b\right)-{\stackrel{\&RightArrow;}{r}}_0\left(s\right)]\&CenterDot;{\hat{e}}_w.$ Particularly, in formula

(49) in, u _C1And u _C2Be respectively applied for expression when using x _c=x _C1And x _C2The time u that obtains _cValue.In formula (48), use u _cReplace x _cCan obtain:

$f_c(x_c,s_a,s_b)={\&Integral;}_{s_a}^{s_b}\mathrm{ds}[w_2(x_{c2}-u_c)+w_1(u_c-x_{c1})][{\&Integral;}_R\frac{d{u^{\&prime;}}_c}{u_c-{u^{\&prime;}}_c}{P}_{\mathrm{\&pi;}}({u^{\&prime;}}_c,s_a,s_b)+C]---\left(50\right)$

Wherein, for given u ' _c, can determine x ' by use formula (49) _c,

And x ' _cThrough type (30) is associated x ' _cAnd u ' _cThrough type (49) is associated, and

$({u^{\&prime;}}_d,{v^{\&prime;}}_d,-S\left(s\right))={\stackrel{\&RightArrow;}{r}}_0\left(s\right)-({\stackrel{\&RightArrow;}{r}}^{\&prime;}-{\stackrel{\&RightArrow;}{r}}_0\left(s\right))\frac{S\left(s\right)}{({\stackrel{\&RightArrow;}{r}}^{\&prime;}-{\stackrel{\&RightArrow;}{r}}_0\left(s\right))\&CenterDot;{\hat{e}}_w}---\left(51\right)$

$R_{\mathrm{\&pi;}}({u^{\&prime;}}_c,s_a,s_b)=\frac{\sqrt{(x_{c2}-{x^{\&prime;}}_c)({x^{\&prime;}}_c-x_{c1})}}{w_2(x_{c2}-{x^{\&prime;}}_c)+w_1({u^{\&prime;}}_c-x_{c1})}\frac{{\mathrm{\&Pi;}}_c\left({x^{\&prime;}}_c\right)}{|{\stackrel{\&RightArrow;}{r}}^{\&prime;}-{\stackrel{\&RightArrow;}{r}}_0\left(s\right)|}\mathrm{sgn}[-\widehat{\mathrm{\&beta;}}\&CenterDot;{\hat{e}}_w]\frac{\mathrm{dP}({u^{\&prime;}}_d,{v^{\&prime;}}_d,d)}{\mathrm{ds}}{|}_{\widehat{\mathrm{\&beta;}}}---\left(52\right)$

As can be seen, first expression in the formula (50) is along u ' _cThe Hilbert transform of axle like this, can utilize the FFT technology that the data filtering in the formula (50) is calculated efficiently.Therefore, the algorithm of representing in the formula (50) can be rebuild the image on the string as follows: at detecting device upper edge u ' _cAxle carries out filtering (that is, the one dimension Hilbert transform) to weighted data, then filtered data back projection (that is, to s integration) to string.Because this new method derives from the BPF method, so similar with the BPF method, it also can accurately rebuild image on the string according to truncated data.This is different with the FBP method, and the FBP method can not accurately be rebuild image on the string according to truncated data.

Use the numerical value research of BPF, MFBP and FBP

Provide the quantitative result of numerical value research, be used for proving above theory that proposes and method.At first, shown in Fig. 8 c and 17a, single string is carried out image reconstruction according to the data of using circular arc-arc track to obtain.Subsequently, in the area-of-interest (ROI) of three-dimensional, carry out image reconstruction according to the n-PI data of using helical trajectory to obtain.

Three kinds of above-mentioned methods, BPF in the FBP in the formula (38), the formula (46) and the MFBP in the formula (50) relate to the specified data derivative:

$\frac{\&PartialD;}{\&PartialD;q}D({\stackrel{\&RightArrow;}{r}}_0\left(q\right),\widehat{\mathrm{\&beta;}}){|}_{q=5}---\left(53\right)$

Perhaps of equal valuely:

$\frac{\mathrm{dP}(u_d,v_d,s)}{\mathrm{ds}}{|}_{\widehat{\mathrm{\&beta;}}}---\left(54\right)$

For spiral scan, directly (perhaps of equal valuely, derivative s) may be obscured artifact (aliasing artifact) owing to sparse relatively being easy to generate of visual angle sampling to computational data to λ.The ground in generation, the alternative expressions of the calculating of data derivative can followingly derive:

$\frac{\&PartialD;}{\&PartialD;q}D({\stackrel{\&RightArrow;}{r}}_0\left(q\right),\widehat{\mathrm{\&beta;}}){|}_{q=5}=\frac{\mathrm{dP}(u_d,v_d,s)}{\mathrm{ds}}{|}_{\widehat{\mathrm{\&beta;}}}$

$=(\frac{d{\stackrel{\&RightArrow;}{r}}_0}{\mathrm{ds}}\&CenterDot;{\hat{e}}_u\left(s\right)+\frac{u_d}{S\left(s\right)}\frac{d{\stackrel{\&RightArrow;}{r}}_0\left(s\right)}{\mathrm{ds}}\&CenterDot;{\hat{e}}_w\left(s\right))\frac{A(u_d,v_d)}{{\stackrel{\&RightArrow;}{r}}^{\&prime;}-{\stackrel{\&RightArrow;}{r}}_0\left(s\right)}\frac{\&PartialD;P(u_d,v_d,s)}{{\&PartialD;u}_d}$

$+[\frac{d{\stackrel{\&RightArrow;}{r}}_0\left(s\right)}{\mathrm{ds}}\&CenterDot;{\hat{e}}_v\left(s\right)+\frac{v_d}{S\left(s\right)}\frac{d{\stackrel{\&RightArrow;}{r}}_0\left(s\right)}{\mathrm{ds}}\&CenterDot;{\hat{e}}_w\left(s\right)]\frac{A(u_d,v_d)}{{\stackrel{\&RightArrow;}{r}}^{\&prime;}-{\stackrel{\&RightArrow;}{r}}_0\left(s\right)}\frac{\&PartialD;P(u_d,v_d,s)}{{\&PartialD;v}_d}$

$+\frac{\mathrm{dP}(u_d,v_d,s)}{\mathrm{ds}}{|}_{\stackrel{\&RightArrow;}{r}}---\left(55\right)$

Wherein, A (u _d, v _d) in formula (32), define.In the cone-beam imaging of reality, data are normally along u _dAnd v _dRecord on the equally distributed discrete grid block of axle.Therefore, the expression formula in the use formula (55), data are with respect to u _dAnd v _dDerivative can directly calculate according to measured data, and do not need to use extra interpolation, and in back projection's step, the data derivative in last of formula (55) can calculate by integration with resolving, thereby obtains at s respectively s _aAnd s _bThe border item at place.

In current numerical value research, consider the scanning of Shepp-Logan model by using two kinds of tracks.Suppose that the maximum ellipsoidal central point in the Shepp-Logan model is positioned at the initial point of fixed coordinate system.For scanning one, adopt circular arc-arc track of describing according to Fig. 6 c, wherein, and two circular arcs mutually vertical (α=pi/2), and orbit segment is s ∈ [p _CcPi/2,3p _CcPi/2].For scanning two, adopt the helical trajectory of standard, and on string reconstructed image, these strings are corresponding to so-called 3-PI line; That is s, _a∈ [2 π R ₀, 0], and s _b∈ [s _a+ 2 π R _l, s _a+ 4 π R _l], and ${\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="A20058001234800741.png,A20058001234800881.png"\; state="\{\{state\}\}">R</figure-callout>}}_1^2={\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0^2+{(h/2\mathrm{\&pi;})}^2.$ Two kinds of tracks of this that considered all satisfy condition (2).According to the Shepp-Logan model, use these two kinds of tracks to generate two groups of cone beam data.For circular arc-arc track, 2 π p _CcThe arc length interval be divided into 1024 points, wherein p _CcBe taken as 570mm.Spacing along helical trajectory is 2 π R ₁/ 1200, R wherein ₀=570mm, pitch h are the every circle of 40mm.Source-detector distance is taken as constant S=1005mm.Adopt the two-dimensional detector plane, it is made up of 512 * 256 square detector cells.The minor face of rectangle detector plane is along the z axle, and the size of square detector cell is 0.78mm * 0.78mm.

In order to prove the dirigibility of string method for reconstructing, used circular arc-circular arc source track.Example only shows the result by adopting the BPF method to obtain hereto.Adopt MFBP and FBP method also can obtain similar result.Figure 17 a shows this circular arc-arc track, and its surface is by fixing s _a=0.04 π p _Cc, and in whole interval [0,3 π p _Cc/ 2] go up scanning (sweep) s _bAnd produce.Thick line segment table among Figure 17 a shows by s _a=-0.04 π p _CcAnd s _b=0.98 π p _CcThe string of regulation.Figure 17 b is the reconstructed image that comprise Figure 17 a shown in surface of Shepp-Logan model on string.Quantitative coincideing has been shown among Figure 17 c.Particularly, Figure 17 c shows reconstruction (solid line) image of the string shown in Figure 17 a and the profile of true (dotted line) image, reconstructed image on the string and corresponding true picture are compared, and the precision that is used on the string of a musical instrument, carrying out the algorithm of image reconstruction of proving institute proposition.

ROI in the three-dimensional body (for example, support cylinder) can resolve into gang's straight-line segment arbitrarily.When these line segments were positioned on the string of a musical instrument of track of satisfy condition (1) and (2), these method for reconstructing just can be used for accurately rebuilding the image on the string, therefore can be used to rebuild the exact image in the ROI.For traditional helical trajectory, string (n-1) π R that serves as reasons ₁≤ s _b-s _a≤ (n+1) π R ₁The n-PI line segment of regulation, wherein n is an odd number.Especially, for n=1, string becomes the PI line segment.

As example, provide BPF and the MFBP method used below, the image reconstruction that in ROI, carries out according to the 3-PI data of using traditional helical trajectory to obtain.Rebuild problem in order to simulate 3-PI, in two circles (turn) along the source track cone beam data of on 2400 visual angles, sampling.Also generated noise data by in noise free data, adding Gaussian noise.The standard deviation of Gaussian noise is selected as the peaked 0.1% of noise free data, so that the low-down contrast structure in the Shepp-Logan model can not covered fully by data noise.

With reference to Figure 18 a-b, show and use the BPF method (Figure 18 a) and noise 3-PI data (Figure 18 b) are arranged, to use the image of the Shepp-Logan model that string rebuilds according to the noiseless 3-PI data that generated respectively.In Figure 18 a and 18b, the image of left column, middle column, right row lays respectively at by x=0cm, on the two-dimentional tangent plane (slice) of y=-2.7cm and z=0cm regulation.Display window is [1.0,1.05].With reference to Figure 19 a-b, show and use the MFBP method (Figure 19 a) and noise 3-PI data (Figure 19 b) are arranged, to use the image of the Shepp-Logan model that the string of a musical instrument rebuilds according to the 3-PI data that generated.(a) and the image in the left column (b), middle column, the right row lay respectively at by x=0cm, on the two-dimentional tangent plane of y=-2.7cm and z=0cm regulation.Display window is [1.0,1.05].Similar result also can use the FBP method to obtain, though do not illustrate here.These results represent that the algorithm that is proposed can accurately rebuild the image on the 3-PI line (that is string).

In order to compare, also BPF method and MFBP method are applied to according to the image of rebuilding in the data that generate on two circles on the PI line segment, it is respectively shown in Figure 20 a-b and Figure 21 a-b.Equally, the image among Figure 20 a, 21a and Figure 20 b, the 21b is respectively according to noise free data with there is noise data to obtain.Image in left column among Figure 20 a and the 20b, middle column and the right row lays respectively at by x=0cm, on the two-dimentional tangent plane of y=-2.7cm and z=0cm regulation.Display window is [1.0,1.05].Image in left column among Figure 21 a and the 21b, middle column and the right row lays respectively at by x=0cm, on the two-dimentional tangent plane of y=-2.7cm and z=0cm regulation.Display window is [1.0,1.05].Observe these accompanying drawings, find out easily, these methods can accurately be rebuild the image on the PI line segment (that is string).For the fixing number of turn, as can be seen, the three-dimensional ROI that can be only rebuilds based on the 3-PI line segment is than can be little based on the three-dimensional ROI that the PI line segment is rebuild.This can be understood as, for filling given ROI, and usually need be than the more 3-PI line segment of PI line segment (that is, more multiturn).

The PET imaging

As discussed earlier, the PET imaging is a kind of diagnostic imaging process, the metabolic activity of each tract that it can evaluation object (for example, human body) and the level of perfusion.Some present PET imaging systems adopt columned structure, wherein adopt discrete detecting unit, and these detecting units are set to form the stacked structure of circular detector ring.In order to use this geometry also to design the PET method for reconstructing of resolving.Yet, also can use cylindrical-shaped structure structure in addition.

Researched and developed PET system based on the detecting device panel.For example, the PENN-PET system is made up of plane monocrystal NaI (T1) detecting device of six hexagonal array.In exemplary C-PET scanner, these flat boards are replaced by the NaI of curved surface (T1) plate.Also can use the detecting device of other type.In addition, also considered to use traditional gamma camera to carry out consistance imaging (coincidence imaging).The detecting device panel can be used for the PET imaging device of toy and specific use.For example, special-purpose PEM (positron emission mammography (positron emission mammography)) system and prostate imaging device are normally based on using two opposed planes or curved surface detecting device panel.

Using an advantage of detecting device panel in the PET system is its cost efficiency.Large tracts of land panel with high aggregation rate can be with relatively low cost manufacturing, with obtain the to have good axial extension PET system of (thereby have detection sensitivity through improving and the imaging volume range of increase).The use of detecting device panel also makes it possible to carry out modular PET system design, and structure flexibly is provided thus, these flexibly structure can under the image-forming condition that constantly changes, be used to realize optimum imaging.Large-area detecting device panel can be used to carry out the high-performance imaging of object, for example the PET imaging of toy or special applications.

Image reconstruction based on the PET system of panel adopts iterative technique or traditional analytical algorithm to realize.The iterative technique of three-dimensional PET imaging has bigger calculated amount usually, and on the other hand, the common efficient of analytical algorithm is higher.Yet traditional analytical algorithm is developed for being used for cylindric PET system; Therefore, before reconstruction based on the system of panel, must be on circular cylindrical coordinate with the data interpolating that obtained.This is handled, and (for example, in the small animal position emission tomography (PET) system) may cause serious resolution loss in high resolution imaging apparatus.In addition, the validity of existing analytical algorithm and precision depend on and satisfy quite strict image-forming condition.These conditions are difficult to satisfy for the PET system based on panel usually.(for example, may there be very big gap usually between the adjacent panel, thus the disappearance of the data when causing hole chamber X line to be taken pictures, and cause in image, producing counterfeit batten line.)

Reconstruction based on string can improve the PET imaging.For example, rebuild for cone-beam, above disclosed method allows to use common source track, and can accurately or substantially accurately carry out ROI according to less data and rebuild.This ROI imaging capability may be useful for wherein using the low coverage scanner to obtain the specific use imaging of data at each position and visual angle.On the contrary,, can study the image that is used to produce specific regulation ROI, reduce radiological dose simultaneously or avoid imaging arrangement the irradiation of vitals by these general method for reconstructing.

Method for reconstructing discussed above (for example, the X ray cone beam reconstruction techniques) can be generalized to the PET system, to produce the analytic reconstruction method of brand-new type.Because the source track smooth any continuous path that can be segmentation C1, so these technology can be applied to PET system () legacy data coordinate for example, based on the PET system of panel, and not needing data interpolating to specific preferred coordinate.Therefore, can eliminate a source of the resolution loss in traditional parsing PET reconstruction.In addition,, these methods rebuild, so, can avoid the reconstruction problem that causes owing to out of order detecting unit or detecting device gap for some ROI because allowing accurately to carry out ROI according to the less data that satisfy specified conditions.The performance of these methods (for example, picture noise characteristic, spatial resolution) is discussed below.

In addition, these new technologies can be used for studying modular design idea, and wherein, the structure of PET system is very flexible, thereby obtain optimal performance under the image-forming condition that changes.For example, these method for reconstructing make it possible to rebuild carry out before, check that whether given structure can produce accurate the reconstruction at the ROI of regulation.Therefore, if a given imaging task then can be developed operable multiple suitable structure, and therefrom select to satisfy those structures of specified conditions (for example, peak response).

In PET, each can limit a bar response line (LOR) to detecting unit, and this line of response is generally defined as the line at the center in the front that connects these two detecting units.Suppose desirable spatial resolution, the consistance counting of the expection of being measured by the PET scanner equals the line integral that distributes along the radioactivity (activity) of the LOR of this scanner.Comparatively speaking, the line integral that produces in the imaging of X ray cone-beam is limited by the line that connects x-ray source and X-ray detector.Therefore, each detecting unit in the PET system can be regarded " source " or the virtual source in the cone-beam geometric configuration as, and regards other detecting units as detecting device.Setting up this connection (will discuss in more detail below) afterwards, reconstruction technique discussed above can be promoted the three-dimensional PET reconstruction algorithm of parsing that is used for producing brand-new type at an easy rate.

Only as an example, X ray cone-beam method for reconstructing discussed above can be generalized to and is used for any PET scanner structure.Yet,, shown in Figure 22 b, considered the PET system that constitutes by four area detector panels as specific example.The sampling that the LOR that is produced by this scanner structure can not provide convenience on original coordinate, this original coordinate are to adopt in the analytic method of developing for the data that cylindric PET system is produced are reconstructed.Though can carry out interpolation (rebinned) to data,, comprise that still this processing is relatively good for fear of reducing resolution.

Figure 22 a shows in two-dimensional rectangle PET system the example by the fan-beam data that the LOR that is associated with given detecting unit (A or B) is divided into groups to generate.By detecting unit is advanced along detecting device face (being represented by arrow), can obtain effective virtual source track.In this case, there is unique non-trivial (non-trivial) source track.Therefore, Figure 22 a shows and how two-dimensional PE T data is divided into groups again or be organized as the fan-beam data.The LOR that is associated with given detecting unit has formed the fan-beam data, and this detecting unit serves as " source ".Can be by making this source position at detecting device face go forward into acquisition " source track " or virtual source track.By the two-dimensional rectangle system, this unique non-trivial track is by four continuous rectilinear(-al)s.When being generalized to three-dimensional four sides plate rectangle PET system, the LOR that is associated with given detecting unit can form cone beam data now.Yet in this case, the source track no longer is unique.In fact, any continuous path that limits on these four detecting device panels all is an active path.Figure 22 b shows the virtual source track that obtains on the detecting device panel by spiral path is projected to.The pitch of this spiral path can change, thereby defines different tracks.This different track also can generate by axis translation one track along scanner.The track that shows among Figure 22 b is different with widely used common helical trajectory in the imaging of X ray cone-beam: they comprise the continuous line segment that contains bending.But it doesn't matter, and parsing cone beam reconstruction techniques discussed above can directly apply to these tracks.

By these cone beam reconstruction techniques, different paths causes different reconstruction algorithm, and the zones of different (because uncertainty of statistics) that usually generation can accurate reconstruction.For example, use the screw with long screw pitch track and the algorithm that obtains can be corresponding with the reconstruction that obtains by the consistance data that comprise bigger ring difference.On the contrary, can also therefore obtain the accurate reconstruction of given ROI by adopting different source tracks according to the different subclass of fetched data.By suitably limiting many virtual source tracks and, can when rebuilding, considering all measurement data, thereby reduce noise to averaging by the result who uses these trajectory generation.As follows, the reconstruction of using this track has been shown in Figure 22 b.Yet this reconstruction algorithm can be applied to common track.

Reconstruction based on string can be used for image reconstruction.For example, backprojection-filtration (BPF) method and minimum data filtered back projection (MFBP) method can be used for carrying out image reconstruction according to the cone beam data of using common track to obtain.These methods go for using the data for projection of the track collection with bending.Shown in above Figure 22 a and 22b, the cone beam data that can be interpreted as using virtual track to obtain by the data that obtain based on the PET system of panel with singular point.Therefore, the method for carrying out image reconstruction according to cone beam data can easily be applied to based in the image reconstruction in the PET system of panel.

Shown in Figure 22 b, plate PET system can design effective virtual track for the four sides

The sectionally smooth function that this effective virtual track is λ, and have a plurality of singular points in the junction of two adjacent panels.For designed track, the string of a musical instrument can be defined in two points

With

Place and the crossing straight line of this effective virtual track.Alternatively, string can be defined in two points

With

Place and the crossing curve of this effective virtual track.As previously mentioned, on the string of a musical instrument with

With

Can one type string as the line segment of end points.Can use:

${\hat{e}}_c=\frac{{\stackrel{\&RightArrow;}{r}}_0\left({\mathrm{\&lambda;}}_b\right)-\stackrel{\&RightArrow;}{r}\left({\mathrm{\&lambda;}}_a\right)}{|{\stackrel{\&RightArrow;}{r}}_0\left({\mathrm{\&lambda;}}_b\right)-\stackrel{\&RightArrow;}{r}\left({\mathrm{\&lambda;}}_a\right)|}---\left(56\right)$

The direction of representing this string of a musical instrument.Formula (56) is similar to formula (5).The object function Cone beam projection on mathematics, can be expressed as:

$P(u_d,v_d,\mathrm{\&lambda;})={\&Integral;}_0^{\&infin;}\mathrm{dtf}({\stackrel{\&RightArrow;}{r}}_0\left(\mathrm{\&lambda;}\right)+t\widehat{\mathrm{\&beta;}})---\left(57\right)$

Wherein, vector of unit length

Be illustrated in (u _d, v _d) locate the direction of the specific X ray that intersects with detector plane.Source and subpoint (u _d, v _d) between distance can pass through $A(u_d,v_d)=\sqrt{{\mathrm{<figure-callout\; id="2"\; label="u\; d"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">u</figure-callout>}}_d^{}+{\mathrm{<figure-callout\; id="2"\; label="v\; d"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">v</figure-callout>}}_d^{}+{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">S</figure-callout>}}^2}$ Calculate, wherein S represents that the source arrives the distance of detecting device.

Method discussed above can be rebuild the image on the string.The example of these methods comprises BPF and MFBP.Similar to the front at the discussion of BPF method, establish x _C1And x _C2Two end points of expression string, and establish [x _A, x _B]  [x _C1, x _C2].In addition, modified data function can be defined as:

$P^{\&prime;}({u^{\&prime;}}_d,{v^{\&prime;}}_d,\mathrm{\&lambda;})=-[\frac{d{\stackrel{\&RightArrow;}{r}}_0}{\mathrm{d\&lambda;}}\&CenterDot;\widehat{\mathrm{\&beta;}}]P({u^{\&prime;}}_d,{v^{\&prime;}}_d,\mathrm{\&lambda;})$

$+A({u^{\&prime;}}_d,{v^{\&prime;}}_d)\frac{d{\stackrel{\&RightArrow;}{r}}_0}{\mathrm{d\&lambda;}}\&dtri;u_d{v}_{d}P({u^{\&prime;}}_d,{v^{\&prime;}}_d,\mathrm{\&lambda;})---\left(58\right)$

The BPF method can be provided by following formula on mathematics:

$f\left(\stackrel{\&RightArrow;}{r}\right)=\frac{f_{\mathrm{bp}}\left(\stackrel{\&RightArrow;}{r}\right)+f_{\mathrm{bc}}\left(\stackrel{\&RightArrow;}{r}\right)}{{2\mathrm{\&pi;}}^2\sqrt{(x_B-x_C)(x_C-x_A)}}---\left(59\right)$

Wherein,

$f_{\mathrm{bp}}\left(\stackrel{\&RightArrow;}{r}\right)={\&Integral;}_{x_A}^{x_B}\frac{d{x^{\&prime;}}_c}{x_c-{x^{\&prime;}}_c}\sqrt{(x_B-{x^{\&prime;}}_c)({x^{\&prime;}}_c-x_A)}\&times;{\&Integral;}_{{\mathrm{\&lambda;}}_1}^{{\mathrm{\&lambda;}}_2}\frac{1}{{|{\stackrel{\&RightArrow;}{r}}^{\&prime;}-{\stackrel{\&RightArrow;}{r}}_0|}^2}{P}^{\&prime;}({u^{\&prime;}}_d,{v^{\&prime;}}_d,\mathrm{\&lambda;})---\left(60\right)$

$f_{\mathrm{bc}}\left(\stackrel{\&RightArrow;}{r}\right)=P({\mathrm{<figure-callout\; id="0"\; label="u\; d"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">u</figure-callout>}}_d,{\mathrm{<figure-callout\; id="0"\; label="v\; d"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">v</figure-callout>}}_d,{\mathrm{\&lambda;}}_1)\&times;(\frac{\mathrm{\&pi;}\sqrt{(21-x_B)[21-x_A)}}{21-x_C}+\frac{\mathrm{\&pi;}\sqrt{x_B{x}_A}}{x_C}]---\left(61\right)$

Wherein, $l=|\stackrel{\&RightArrow;}{r}\left({\mathrm{\&lambda;}}_b\right)-\stackrel{\&RightArrow;}{r}\left({\mathrm{\&lambda;}}_a\right)|/2,$

${\stackrel{\&RightArrow;}{r}}^{\&prime;}={\stackrel{\&RightArrow;}{r}}_0\left(\stackrel{\&RightArrow;}{r}\right)+{x^{\&prime;}}_c{\hat{e}}_c,$ x′ _c∈[0，2l](62)

Expression on the string by coordinate x ' _cThe point of determining, u _DoAnd v _DoBe illustrated in anglec of rotation λ ₁The place, point

The position of the cone beam projection on detecting device.Formula (59) is to satisfying x _c∈ (x _A, x _B) any point

All set up.

In addition, similar to above discussion at the MFBP method, this method can be expressed as:

$f\left(\stackrel{\&RightArrow;}{r}\right)={\&Integral;}_{{\mathrm{\&lambda;}}_1}^{{\mathrm{\&lambda;}}_2}\mathrm{d\&lambda;}[(1-u_c){\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">w</figure-callout>}}_2+u_c{w}_1]$

$\&times;{\&Integral;}_{x_A}^{x_B}\frac{d{u^{\&prime;}}_c}{u_c-{u^{\&prime;}}_c}\frac{\sqrt{(x_B-{x^{\&prime;}}_c)({x^{\&prime;}}_c-x_A)}}{(1-{u^{\&prime;}}_c){\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">w</figure-callout>}}_2+{u^{\&prime;}}_{\mathrm{<figure-callout\; id="1"\; label="c\; w"\; filenames="A20058001234800741.png,A20058001234800881.png"\; state="\{\{state\}\}">c</figure-callout>}}{w}_{}{}_1}\&times;\frac{1}{|{\stackrel{\&RightArrow;}{r}}^{\&prime;}-{\stackrel{\&RightArrow;}{r}}_0{|}^2}{P}^{\&prime;}({u^{\&prime;}}_d,{v^{\&prime;}}_d,\mathrm{\&lambda;})$

$+\frac{1}{{2\mathrm{\&pi;}}^2}\frac{1}{\sqrt{(x_B-x_c)(x_c-x_A)}}{f}_{\mathrm{bc}}\left(\stackrel{\&RightArrow;}{r}\right)---\left(63\right)$

Wherein, u _cExpression x _cCone beam projection on detecting device, and itself and x _cThe pass be

Wherein, ${\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="A20058001234800741.png,A20058001234800881.png"\; state="\{\{state\}\}">w</figure-callout>}}_1=-[{\stackrel{\&RightArrow;}{r}}_0\left({\mathrm{\&lambda;}}_1\right)-{\stackrel{\&RightArrow;}{r}}_0\left(\mathrm{\&lambda;}\right)]\&CenterDot;{\hat{e}}_w,$ ${\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">w</figure-callout>}}_2=-[{\stackrel{\&RightArrow;}{r}}_0\left({\mathrm{\&lambda;}}_2\right)-{\stackrel{\&RightArrow;}{r}}_0\left(\mathrm{\&lambda;}\right)]\&CenterDot;{\hat{e}}_w.$ Vector of unit length

Expression is from the direction of the mid point of source direct detection device.

The ROI image reconstruction by using BPF and MFBP method to carry out in the plate PET system of four sides has been showed in following numerical value research.Also can use the PET system of other type and the method for other type.Shown in Figure 22 b, for PET system, can design " square " virtual spiral track with four panels, this effective helix angle track can parameter turn to:

${\stackrel{\&RightArrow;}{r}}_0\left(\mathrm{\&lambda;}\right)=\left\{\begin{array}{cc}{({\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0,2{\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0\mathrm{\&lambda;}-{\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0,\mathrm{h\&lambda;})}^t& \mathrm{\&lambda;}\&Element;\left[\mathrm{0,1}\right]\\ {(-2{\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0\mathrm{\&lambda;}+3{\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0,{\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0,\mathrm{h\&lambda;})}^t& \mathrm{\&lambda;}\&Element;\left[\mathrm{1,2}\right]\\ {(-{\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0,-{2\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0\mathrm{\&lambda;}+{5\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0,\mathrm{h\&lambda;})}^t& \mathrm{\&lambda;}\&Element;\left[\mathrm{2,3}\right]\\ {({2\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0\mathrm{\&lambda;}-{7\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0,-{\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="A20058001234800831.png"\; state="\{\{state\}\}">R</figure-callout>}}_0\mathrm{h\&lambda;})}^t& \mathrm{\&lambda;}\&Element;\left[\mathrm{3,4}\right]\end{array}\right.---\left(64\right)$

Wherein, R ₀Be the distance from a plane to the z axle, the pitch in h and the helical trajectory is similar, and it has determined the speed that this track rises along the z axle.By this track, can be by using R ₀=26.5cm, h=12.8cm is for 1024 visual angles that are evenly distributed among the λ ∈ [0,4], for the Shepp-Logan model generates the cone-beam data for projection.

According to this simulated data, be somebody's turn to do " square " virtual spiral track by using, can use BPF and MFBP method to come reconstructed image.Only provided the result who generates by the BPF method below; Yet, also can use the MFBP method similarly.Figure 23 a and 23b have shown the image that obtains on two groups of selected strings on " square " virtual spiral track at this.In these images, transverse axis is represented the coordinate on each string, that is, and and the x ' in the formula (62) _c, and Z-axis is represented different strings.When display result on these original string coordinates, these images may look different fully with the master pattern that defines in Cartesian coordinate.In Figure 23 a, shown by λ ₁=0 and λ ₂Image on one group of string of ∈ (1,3) appointment.This image looks and comprises two different parts.By the track among procuratorial work Figure 22 b, can see at λ=2 places having bending that this has formed two visibly different portion boundaries in the image.Figure 23 b has also shown by λ ₁=0.5 and λ ₂Image on one group of string of ∈ (2,3) appointment.Because active path is smooth for λ ∈ (2,3), so this image does not demonstrate as observed different part under the situation in front.The image that obtains on original string coordinate can easily be changed, to obtain the image on the Cartesian coordinate.Figure 24 a-c has shown the reconstructed image on the Cartesian coordinate.Particularly, Figure 24 a-c has represented respectively at x=0cm, the image in the plane at y=-2.7cm and z=2.5cm place, and display window is [1.0,1.05].

Redundant letter mouse

As mentioned above, can select track, come ROI is carried out imaging so that can produce enough data.There are the wherein redundant a plurality of examples of data possibility, because these data are duplicating of acquired other data.If the string of source trajectory generation is unnecessary (for example, not filling the string of area-of-interest) for rebuilding ROI, can think that then data are redundant.Can use redundant data to revise the selected characteristic of (for example, improving) image, rather than abandon redundant data simply.Any characteristic of image can use redundant data to revise, and these characteristics include but not limited to: noise, deviation, texture, resolution and variance.

At first can be qualitatively or discern redundant information quantitatively.For example, can discern redundant information qualitatively, whether exceedingly fill area-of-interest to determine string.Particularly, if then may there be redundant data in the one group of string that has collected and not only filled ROI but also filled other zones.In case determine to exist redundant data, just this redundant data can be comprised coming in to revise at least one characteristic.For example, can use weight that redundant data is comprised coming in, will go through below.Alternatively, if treatment of picture is accelerated in expectation, then can abandon this redundant data.

Be to use example below from the scanning among Fig. 7 a-c.Although used two-dimentional ROI in this example, when three-dimensional ROI imaging, can similarly use redundant information.If ROI is included in by λ ₁And λ ₂In the zone that PI line segment of determining and the scanning of this fan-beam are limited, then Bi Yao scanning angle scope is [λ ₁, λ ₂], shown in Figure 25 a.Actual scanning angular range [the λ of the rate of examining as shown in Figure 25 b _Min, λ _Max], if [λ ₁, λ ₂] ∈ [λ _Min, λ _Max], then at angular range [λ _Min, λ ₁) and (λ ₂, λ _Max] data that obtain are for by λ ₁And λ ₂Image reconstruction on the PI line segment of determining comprises redundant information.

The string method for reconstructing can only use [λ ₁, λ ₂] data in the scope rebuild the image on this PI line segment.Needn't use [λ _Min, λ ₁) and (λ ₂, λ _Max] the interior data of scope.

This redundant information can be readily incorporated in the method for reconstructing.For redundant information is comprised coming in, can be at actual scanning angular range [λ _Min, λ _Max] in the data that obtain carry out suitable weighting, make the redundancy section of the data that obtain to the contribution normalization fully of the image on the PI line segment.

Utilize the back projection of the redundant information of data inherence to be expressed as:

$g_{\mathrm{\&pi;}}^{\left(w\right)}({x^{\&prime;}}_{\mathrm{\&pi;}},{\mathrm{\&lambda;}}_1,{\mathrm{\&lambda;}}_2)={\&Integral;}_{{\mathrm{\&lambda;}}_{\min }d}^{{\mathrm{\&lambda;}}_{\max }}\frac{\mathrm{d\&lambda;}}{{|{\stackrel{\&RightArrow;}{r}}^{\&prime;}-{\stackrel{\&RightArrow;}{r}}_0\left)\mathrm{\&lambda;}\right)|}^2}\{-[\frac{d{\stackrel{\&RightArrow;}{r}}_0\left(\mathrm{\&lambda;}\right)}{\mathrm{d\&lambda;}}\&CenterDot;\widehat{\mathrm{\&beta;}}({u^{\&prime;}}_d,\&lambda;)]\left[w({u^{\&prime;}}_d,\mathrm{\&lambda;})P({u^{\&prime;}}_d,\mathrm{\&lambda;})\right]$

$+\left[\frac{d{\stackrel{\&RightArrow;}{r}}_0\left(\mathrm{\&lambda;}\right)}{\mathrm{d\&lambda;}}\right]\&CenterDot;{\hat{e}}_u\left(\mathrm{\&lambda;}\right)\sqrt{{{u^{\&prime;}}_{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">d</figure-callout>}}}^2+{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="A20058001234800761.png"\; state="\{\{state\}\}">S</figure-callout>}}^2}\frac{\&PartialD;\left[w({u^{\&prime;}}_d,\mathrm{\&lambda;})P({u^{\&prime;}}_d,\mathrm{\&lambda;})\right]}{\&PartialD;{u^{\&prime;}}_d}\}$

$+\frac{\left(w({u^{\&prime;}}_d,\mathrm{\&lambda;})P({u^{\&prime;}}_d,\mathrm{\&lambda;})\right)}{\left|{{\stackrel{\&RightArrow;}{r}}^{\&prime;}-\stackrel{\&RightArrow;}{r}}_0\left(\mathrm{\&lambda;}\right)\right|}{|}_{{\mathrm{\&lambda;}}_{\min }}^{{\mathrm{\&lambda;}}_{\max }}---\left(65\right)$

Wherein, weighting function w (u _d, λ) provide by following formula:

w(u _d，λ)+w(u′ _d，λ′)＝1.0，(66)

W (u _dIf, λ)=0 λ＜λ _MinOr λ＞λ _Max(67)

Therefore, formula (65) has constituted the new method that can utilize data redundancy.Shown in (65), integration is from λ _MinTo λ _Max.In addition, the characteristic that needs are revised is depended in the selection of w.For example, improve variance if desired, then can modus ponens (65) to the derivative of w, and this derivative is set to 0, finds the solution w then.As another example, if deviation can be represented as the function of w, then can be by getting the derivative of this departure function for w, and this derivative is set to 0, finds the solution w then, improves deviation.

As mentioned above, there is the several different methods of coming reconstructed image based on the data of being gathered.A kind of method and apparatus that ROI in the object support part of this object support (this ROI for) is carried out imaging comprises: gather the image that is less than enough this object support and carry out quite accurate data of rebuilding, and carry out rebuilding quite accurately of this ROI based on the data of being gathered.As mentioned above, this object support can comprise a zone on the space, and in this zone, object may be non-0, but at this region exterior, object one is decided to be 0.For example, the data of being gathered can comprise truncated data for object support.In addition, for image data, can move with respect to this object support along a track in the source, is less than basic enough data to the object support reconstructed image thereby collect.This track can be following track: fill this ROI by one group of string section that this track limits.In addition,, can control, be less than enough basically data the object support reconstructed image thereby collect to the source for image data.For example, the source controlled to comprise with respect to this object support and move this source, and when moving with respect to this object support, revise at least one characteristic in this source in this source.Modification to this source can for example, reduce the irradiation to the object support beyond this ROI based on this ROI.In addition, can change the range of exposures in this source,, and reduce irradiation, for example not shine basically the ROI outside so that this ROI is fully shone to the modification in this source.The quite accurate ROI reconstruction of generation can comprise carries out filtering to the data of being gathered, and the data through filtering are carried out back projection, to produce Density Distribution.Back projection can comprise that back projection is to by at least a portion that is used for the string of the path limit in the source of image data on ROI.Alternatively, the quite accurate reconstruction of generation ROI can comprise the back projection based on institute's image data, distributes to generate intermediate density, and middle Density Distribution is carried out quite accurate image, for example the volume blank map picture that filtering produces ROI.

The method and apparatus that another kind carries out imaging to the zone of object can comprise: use the emissive source that moves along source path with respect to this object to shine this zone, gather the data relevant with the ray that passes area-of-interest, and, make up this regional image according to the data of being gathered at least in part based on the coordinate system that limits by this source path.Image that should the zone according to the data construct of being gathered can comprise: identification connects the many one group of strings to point along this source path, wherein this group string is filled the volume of the area-of-interest in this object, calculate the density of string epigraph according to the data of being gathered, and make up 3-D view based on image density and source path.This coordinate system can be by following 3 definition: first point relevant with source path, relevant second point (being different from first point) and being formed on the string between first and second thirdly with source path.Extra step can comprise constructed image transformation to Cartesian coordinate.Perhaps constructed image can be in Cartesian coordinate.

The method and apparatus that another kind carries out imaging to the zone of object can comprise: use the emissive source that moves along source path with respect to this object to shine this zone, gather the data relevant, and make up the image on many strings that limit by source path with the ray that passes this object.These strings can comprise the PI line.And the structure of image can comprise: identification connects the many one group of strings to point along source path, wherein this group string is filled the volume of the area-of-interest in this object, calculate image density on the string according to the data of being gathered, and make up 3-D view based on image density and source path.

The method and apparatus that another kind carries out imaging to the zone of object comprises: gather the data relevant with the ray of launching from object, and organize this data according to the detection position that forms the path, wherein this path limit have many strings of the multistage of the volume of filling this described zone of object.Can launch the ray of any type, for example positron emission.In addition, use the positron emission tomography art can comprise: to gather from the data of object emission, and organize this data, so that rebuild ROI based on many strings to the method and apparatus that ROI carries out imaging.The tissue of data can be based on the virtual source of the outside that is chosen in object along the virtual source orbiting motion.In addition, rebuilding this ROI can comprise: identification connects the many one group of strings to point along this virtual source track, wherein should the group string fills the volume of ROI, calculates image density on these strings according to the data of being gathered; And based on described image density structure 3-D view.

The method and apparatus that another kind of area-of-interest to object carries out imaging can comprise: gather the data on the area-of-interest, carry out back projection to produce the central object function based on these data, then middle object function is carried out filtering to produce the quite accurate image of area-of-interest.Back projection can comprise that back projection is to by at least a portion that is used for the string that the path limited in the source of image data on area-of-interest.And this filtering can comprise the use Hilbert transform.In addition, back projection can produce the central object function based on modified data (for example, through the data of weighting), perhaps can be based on the data of unmodified.

The method and apparatus that another kind of area-of-interest to object carries out imaging can comprise: gather truncated data on area-of-interest, and generate quite accurate image reconstruction based on truncated data.There is the several different methods that is used to generate suitable accurate reconstruction, for example truncated data is carried out filtering, and the truncated data through filtering is carried out back projection generate Density Distribution, perhaps for example these data are carried out back projection and generate the central object function, then middle object function is carried out the quite accurate image that filtering generates area-of-interest.In addition, this back projection can comprise that back projection is to by at least a portion that is used for the string that the path limited in the source of image data on area-of-interest.

It is exemplary that preceding detailed description should be considered to, rather than restrictive, and should be appreciated that, following claim (comprising all equivalents) is intended to limit scope of the present invention.

Claims (110)

1, a kind of at least a portion imaging method to area-of-interest (ROI), this method comprises:

Described at least a portion of described ROI is resolved into string; And

Rebuild described at least a portion of described ROI based on described string.

2, method according to claim 1 is characterized in that, the described at least a portion of rebuilding described ROI comprises quite accurately rebuilds described at least ROI.

3, method according to claim 1 is characterized in that, described at least a portion of described ROI is resolved into string comprise and compile one group of string of filling described ROI.

4, method according to claim 1 is characterized in that, described ROI is two-dimentional.

5, method according to claim 1 is characterized in that, described ROI is three-dimensional.

6, method according to claim 1 is characterized in that, string comprise 2 be connected this straight line of 2.

7, method according to claim 1 is characterized in that, described string comprises the PI line.

8, method according to claim 6 is characterized in that, described ROI comprises at least a portion of object; And

Wherein, described string is with respect to the track definition of described object by the source.

9, method according to claim 8 is characterized in that, rebuilds described ROI and comprises:

Identification connects one group of string of the paired point on the described track, and wherein, this group string is filled the volume of ROI;

According to the image density on the described string of the data computation of obtaining; And

Make up 3-D view based on described image density.

10, method according to claim 9 is characterized in that, object support comprises the territory in the space, and object can be non-zero in this territory, and is decided to be zero at this overseas object one;

Wherein, described ROI is the part of described object support; And

Wherein, the data of being obtained are less than the required data of image of quite accurately rebuilding described object support.

11, method according to claim 10 is characterized in that, the selection source makes the data of obtaining be less than the required data of image of quite accurately rebuilding described object support with respect to the track of described object

12, method according to claim 11 is characterized in that, described track comprises helical trajectory.

13, method according to claim 10 is characterized in that, selects at least one characteristic in source, makes the data of being obtained be less than the required data of image of quite accurately rebuilding described object support.

14, method according to claim 1 is characterized in that, the described at least a portion of rebuilding described ROI based on described string comprises:

Distribute to generate intermediate density based on the data back projection that obtains; And

Middle Density Distribution is carried out filtering, to create the quite accurate image of described area-of-interest.

15, method according to claim 1 is characterized in that, the described at least a portion of rebuilding described ROI based on described string comprises:

To the data filtering of obtaining; And

The described data through filtering of back projection are to generate Density Distribution.

16, method according to claim 15 is characterized in that, the data of being obtained comprise the data of blocking; And

Wherein, the data filtering of being obtained is comprised the data filtering of blocking described.

17, method according to claim 1 is characterized in that, described imaging comprises calculating computed tomography.

18, a kind of equipment of at least a portion imaging to area-of-interest (ROI), this equipment comprises the logic that is used for following processing:

Described at least a portion of described ROI is resolved into string; And

Rebuild described at least a portion of described ROI based on described string.

19, equipment according to claim 18 is characterized in that, the logic of rebuilding described at least a portion of described ROI comprises the logic of quite accurately rebuilding described at least ROI.

20, equipment according to claim 18 is characterized in that, the logic that described at least a portion of described ROI is resolved into string comprises the logic of compiling one group of string of filling described ROI.

21, equipment according to claim 18 is characterized in that, described ROI is two-dimentional.

22, equipment according to claim 18 is characterized in that, described ROI is three-dimensional.

23, equipment according to claim 18 is characterized in that, string comprise 2 be connected this straight line of 2.

24, equipment according to claim 18 is characterized in that, described string comprises the PI line.

25, equipment according to claim 23 is characterized in that, described ROI comprises at least a portion of object; And

Wherein, described string is with respect to the track definition of described object by the source.

26, equipment according to claim 25 is characterized in that, the logic of rebuilding described ROI comprises the logic that is used for following processing:

Identification connects one group of string of the paired point on the described track, and wherein, this group string is filled the volume of described ROI;

According to the image density on the described string of the data computation of being obtained; And

Make up 3-D view based on described image density.

27, equipment according to claim 26 is characterized in that, object support comprises the territory in the space, and object can be non-zero in this territory, and is decided to be zero at this overseas object one;

Wherein, described ROI is the part of described object support; And

Wherein, the data of being obtained are less than the required data of image of quite accurately rebuilding described object support.

28, equipment according to claim 27 is characterized in that, the selection source makes the data of being obtained be less than the required data of image of quite accurately rebuilding described object support with respect to the track of described object.

29, equipment according to claim 28 is characterized in that, described track comprises helical trajectory.

30, equipment according to claim 27, at least one characteristic in selection source makes the data of being obtained be less than the required data of image of quite accurately rebuilding described object support.

31, equipment according to claim 18 is characterized in that, the logic of rebuilding described at least a portion of described ROI based on described string comprises the logic that is used for following processing:

Distribute to generate intermediate density based on the data back projection that is obtained; And

Middle Density Distribution is carried out filtering, to create the quite accurate image of described area-of-interest.

32, equipment according to claim 18 is characterized in that, the logic of rebuilding described at least a portion of described ROI based on described string comprises the logic that is used for following processing:

To the data filtering of being obtained; And

The described data through filtering of back projection are to generate Density Distribution.

33, equipment according to claim 32 is characterized in that, the data of being obtained comprise the data of blocking; And

Wherein, the data filtering of being obtained is comprised the data filtering of blocking described.

34, equipment according to claim 18 is characterized in that, described imaging comprises calculating computed tomography.

35, a kind of described ROI is the part of described object support to the area-of-interest in the object support (ROI) imaging method, and this method comprises:

Image data, these data are less than the data of the image that is enough to quite accurately to rebuild described object support; And

Generate rebuilding quite accurately of described ROI based on the data of being gathered.

36, method according to claim 35 is characterized in that, described ROI is two-dimentional.

37, method according to claim 35 is characterized in that, described ROI is three-dimensional.

38, method according to claim 35 is characterized in that, described object support comprises the territory in the space, and object can be non-zero in this territory, and is decided to be zero at this overseas object one.

According to the described method of claim 38, it is characterized in that 39, the data of being gathered comprise the data of blocking that are used for described object support.

40, method according to claim 35 is characterized in that, image data is included in respect to moving source on the track of described object support, makes to collect the data of lacking than the data of the image that is enough to quite accurately to rebuild described object support.

41, according to the described method of claim 40, it is characterized in that, select described track, make and fill described ROI by one group of string section of described track definition.

42, method according to claim 35 is characterized in that, image data comprises to be controlled the source, makes to collect the data of lacking than the data of the image that is enough to roughly to rebuild described object support.

43, according to the described method of claim 42, it is characterized in that, the source is controlled comprised:

Move described source with respect to described object support; And

When move with respect to described object support in described source, change at least one characteristic in described source.

According to the described method of claim 43, it is characterized in that 44, at least one characteristic that changes described source is based on described ROI's.

According to the described method of claim 43, it is characterized in that 45, the characteristic of the change in described source is selected from such group, this group comprises that the intensity in range of exposures, source and the spectrum in source distribute.

46, according to the described method of claim 43, it is characterized in that, change the irradiation of described at least one characteristic minimizing in described source the object support beyond the described ROI.

47, according to the described method of claim 46, it is characterized in that, change described at least one characteristic and comprise the range of exposures that changes described source, make described ROI be irradiated to substantially, and not illuminated substantially beyond the described ROI.

48, according to the described method of claim 42, it is characterized in that, described source is controlled comprised selectivity characteristic, make that the irradiation to the object support beyond the ROI obtains reducing.

49, method according to claim 35 is characterized in that, quite accurate reconstruction that generates described ROI comprises:

To the data filtering of gathering; And

The described data through filtering of back projection are to generate Density Distribution.

According to the described method of claim 49, it is characterized in that 50, back projection comprises back projection at least a portion by the string of the path definition in source, the path in described source is used for gathering the data about described ROI.

51, method according to claim 35 is characterized in that, quite accurate reconstruction that generates described ROI comprises:

Distribute to generate intermediate density based on the data back projection of being gathered; And

Middle Density Distribution is carried out filtering, to create the quite accurate image of described ROI.

52, a kind of equipment to the area-of-interest in the object support (ROI) imaging, described ROI is the part of described object support, this equipment comprises the logic that is used for following processing:

Image data, described data are less than the data of the image that is enough to quite accurately to rebuild described object support; And

Generate rebuilding quite accurately of described ROI based on the data of being gathered.

According to the described equipment of claim 52, it is characterized in that 53, described ROI is two-dimentional.

According to the described equipment of claim 52, it is characterized in that 54, described ROI is three-dimensional.

According to the described equipment of claim 52, it is characterized in that 55, described object support comprises the territory in the space, object can be non-zero in this territory, and is decided to be zero at this overseas object one.

According to the described equipment of claim 55, it is characterized in that 56, the data of being gathered comprise the data of blocking that are used for described object support.

57, according to the described equipment of claim 52, it is characterized in that, the described logic that is used for image data comprises such logic, and this logic is used for moving source on respect to the track of described object, makes to collect the data of lacking than the data of the image that is enough to roughly to rebuild described object support.

58, according to the described equipment of claim 57, it is characterized in that, select described track, make and fill described ROI by one group of string section of described track definition.

According to the described equipment of claim 52, it is characterized in that 59, the described logic that is used for data acquisition comprises such logic, this logic is used for the source is controlled, and makes to collect the data of lacking than the data of the image that is enough to roughly to rebuild described object support.

According to the described equipment of claim 56, it is characterized in that 60, the logic that is used to control described source comprises the logic that is used for following processing:

Move described source with respect to described object support; And

When move with respect to described object support in described source, change at least one characteristic in described source.

According to the described equipment of claim 60, it is characterized in that 61, the described logic that is used to change at least one characteristic in described source is based on described ROI's.

According to the described equipment of claim 60, it is characterized in that 62, the characteristic of the change in described source is selected from such group, this group comprises that the intensity in range of exposures, source and the spectrum in source distribute.

63, according to the described equipment of claim 60, it is characterized in that, change the irradiation of described at least one characteristic minimizing in described source the object support beyond the described ROI.

64, according to the described equipment of claim 63, it is characterized in that the described logic that is used to change described at least one characteristic comprises such logic, the range of exposures in this described source of logical changes, make described ROI be irradiated to substantially, and not illuminated substantially beyond the described ROI.

According to the described equipment of claim 59, it is characterized in that 65, the logic that is used to control described source comprises such logic, this logic is selected described characteristic, makes that the irradiation to the object support beyond the described ROI obtains reducing.

According to the described equipment of claim 52, it is characterized in that 66, the quite accurate logic of rebuilding that is used to generate described ROI comprises the logic that is used for following processing:

To the data filtering of gathering; And

The described data through filtering of back projection are to generate Density Distribution.

67, according to the described equipment of claim 66, it is characterized in that, the described logic that is used for back projection comprises such logic, and this logical inverse projects at least a portion by the string of the path definition in source, and the path in described source is used for gathering the data about described ROI.

According to the described equipment of claim 52, it is characterized in that 68, the described quite accurate logic of rebuilding that is used to generate described ROI comprises the logic that is used for following processing:

Distribute to generate intermediate density based on the data back projection of being gathered; And

Middle Density Distribution is carried out filtering, to create the quite accurate image of described ROI.

69, a kind of method of the regional imaging to object, this method comprises:

Shine described zone with emissive source, described emissive source moves along the source path with respect to described object;

The data of the emitting substance of area-of-interest transmission are passed in collection; And

At least in part based on the coordinate system of described source path definition, according to the image in the described zone of data construct of gathering.

According to the described method of claim 69, it is characterized in that 70, constructed image comprises volume blank map picture.

71, according to the described method of claim 69, it is characterized in that,, comprise according to the image in the described zone of data construct of gathering based on the coordinate system of described source path definition:

Identification connects one group of string of the paired point on the described source path, and wherein, this group string is filled the volume of area-of-interest in the described object;

According to the image density on the data computation string of being gathered; And

Make up 3-D view based on described image density and described source path.

According to the described method of claim 69, it is characterized in that 72, described coordinate system is defined by following three points: first point relevant with described source path; Second point relevant with described source path, that be different from described first point; The 3rd point on the string that forms between described first point and second point.

73, according to the described method of claim 72, this method also comprises that be Cartesian coordinate to the image transitions that makes up.

74, a kind of equipment of the regional imaging to object, this equipment comprises the logic that is used for following processing:

Shine described zone with emissive source, described emissive source moves along the source path with respect to described object;

The data of the emitting substance of area-of-interest transmission are passed in collection; And

Based on the coordinate system of described source path definition, according to the image in the described zone of data construct of gathering.

According to the described equipment of claim 74, it is characterized in that 75, constructed image comprises the image that volume is filled.

According to the described equipment of claim 74, it is characterized in that 76, the described coordinate system that is used for based on the definition of described source path comprises the logic that is used for following processing according to the logic of the image in the described zone of data construct of gathering:

Identification connects one group of string of the paired point on the described source path, and wherein, this group string is filled the volume of area-of-interest in the described object;

According to the image density on the described string of gathering of data computation; And

Make up 3-D view based on described image density and described source path.

According to the described equipment of claim 74, it is characterized in that 77, described coordinate system is defined by following three points: first point relevant with described source path; Second point relevant with described source path, that be different from described first point; The 3rd point on the string that forms between described first point and second point.

78, according to the described equipment of claim 77, this equipment also comprises the logic that is used for the image transitions that makes up is become Cartesian coordinate.

79, a kind of method of the regional imaging to object, this method comprises:

Shine described zone with emissive source, described emissive source moves along the source path with respect to described object;

The data of the emitting substance of described object transmission are passed in collection; And

According to a plurality of string design of graphics pictures by described source path definition.

According to the described method of claim 79, it is characterized in that 80, described image comprises 3-D view.

According to the described method of claim 79, it is characterized in that 81, described string comprises the PI line.

According to the described method of claim 79, it is characterized in that 82, design of graphics looks like to comprise:

Identification connects one group of string of the paired point on the described source path, and wherein, this group string is filled the volume of area-of-interest in the described object;

According to the image density on the described string of the data computation of being gathered; And

Make up 3-D view based on described image density and described source path.

83, a kind of equipment of the regional imaging to object, this equipment comprises:

Shine the device in described zone with emissive source, described emissive source moves along the source path with respect to described object;

Be used to gather the device of the data of the ray that passes described object transmission; And

Be used for device according to a plurality of string design of graphics pictures that define by described source path.

84,3 described equipment according to Claim 8 is characterized in that described image comprises 3-D view.

85,3 described equipment according to Claim 8 is characterized in that described string comprises the PI line.

86,3 described equipment according to Claim 8 is characterized in that the device that is used for the design of graphics picture comprises:

Identification connects the device of one group of string of the paired point on the described source path, and wherein, this group string of a musical instrument is filled the volume of area-of-interest in the described object;

Be used for device according to the image density on the described string of the data computation of being gathered; And

Device based on described image density and described source path structure 3-D view.

87, a kind of method of the regional imaging to object, this method comprises:

The data of the emitting substance that collection is sent from described object; And

Organize described data according to the detection position that forms the path, wherein said path definition have a string of section of the volume in the described zone of filling described object.

88,7 described methods according to Claim 8 is characterized in that the emitting substance that sends from described object is the positron emission thing.

89, the imaging of a kind of use positron emission is to area-of-interest (ROI) imaging method, and this method comprises:

The data that collection is launched from described object; And

Organize described data so that rebuild described ROI based on string.

90,9 described methods according to Claim 8 is characterized in that, organize described data based on: select a virtual source in that described object is outside, this source is along virtual source orbiting motion.

According to the described method of claim 90, it is characterized in that 91, described string is by described virtual source track definition; And

Wherein, rebuilding described ROI comprises:

Identification connects one group of string of the paired point on the described virtual source track, and wherein this group string is filled the volume of described ROI;

According to the image density on the described string of the data computation of being gathered; And

Make up 3-D view based on described image density.

92, the imaging of a kind of use positron emission is to the equipment of area-of-interest (ROI) imaging, and this equipment comprises:

The device of the data that collection is launched from described object; And

Organize described data so that rebuild the device of described ROI based on string.

93, according to the described equipment of claim 92, it is characterized in that, the device of organizing described data based on: select a virtual source in that described object is outside, this source is along virtual source orbiting motion.

According to the described equipment of claim 93, it is characterized in that 94, described string is by described virtual source track definition; And

Wherein, rebuilding described ROI comprises:

Identification connects the device of one group of string of the paired point on the described virtual source track, and wherein this group string is filled the volume of described ROI;

Device according to the image density on the described string of the data computation of being gathered; And

Make up the device of 3-D view based on described image density.

95, a kind of area-of-interest imaging method to object, this method comprises:

Collection is about the data of area-of-interest;

Carry out back projection based on described data, with the object function in the middle of producing; And

To the object function filtering of this centre, to create the quite accurate image of described area-of-interest.

According to the described method of claim 95, it is characterized in that 96, back projection comprises back projection at least a portion of the string that is defined by source path, this source path is used for gathering the data about described area-of-interest.

According to the described method of claim 95, it is characterized in that 97, filtering comprises the use Hilbert transform.

98, according to the described method of claim 95, this method also comprises makes amendment to the data of being gathered; And wherein, back projection comprises that the data that back projection revised produce middle object function.

99, a kind of equipment of the region of interest domain imaging to object, this equipment comprises the logic that is used for following processing:

Collection is about the data of area-of-interest;

Carry out back projection based on described data, with the object function in the middle of producing; And

To this intermediate density distribution filtering, to create the quite accurate image of described area-of-interest.

100, according to the described equipment of claim 99, it is characterized in that, the logic that is used for back projection comprises such logic, and this logic is used for back projection's at least a portion to the string that is defined by source path, and this source path is used for gathering the data about described area-of-interest.

According to the described equipment of claim 100, it is characterized in that 101, the logic that is used for filtering comprises the logic of using Hilbert transform.

102, according to the described equipment of claim 99, this equipment also comprises the logic that the data of being gathered are made amendment; And the logic that wherein, is used for back projection comprises the logic of data that back projection the revised object function in the middle of producing.

103, a kind of area-of-interest imaging method to object, this method comprises:

Collection is about the data of blocking of area-of-interest; And

Based on described data of blocking, carry out rebuilding quite accurately of image.

According to the described method of claim 103, it is characterized in that 104, quite accurate reconstruction of carrying out image based on described data of blocking comprises:

To the described data filtering of blocking; And

The data of blocking that backprojection-filtration is crossed are to generate Density Distribution.

According to the described method of claim 104, it is characterized in that 105, back projection comprises back projection at least a portion of the string that is defined by source path, this source path is used for gathering the data about described area-of-interest.

According to the described method of claim 103, it is characterized in that 106, quite accurate reconstruction of carrying out image based on described data of blocking comprises:

The described data of back projection are with the object function in the middle of generating; And

To the object function filtering of described centre, to create the quite accurate image of described area-of-interest.

107, a kind of equipment of the region of interest domain imaging to object, this equipment comprises the logic that is used for following processing:

Collection is about the data of blocking of area-of-interest; And

Based on described data of blocking, carry out rebuilding quite accurately of image.

According to the described equipment of claim 107, it is characterized in that 108, quite accurate reconstruction of carrying out image based on described data of blocking comprises:

To the described data filtering of blocking; And

The data of blocking that backprojection-filtration is crossed are to generate Density Distribution.

According to the described equipment of claim 108, it is characterized in that 109, back projection comprises back projection at least a portion of the string that is defined by source path, this source path is used for gathering the data about described area-of-interest.

According to the described equipment of claim 107, it is characterized in that 110, quite accurate reconstruction of carrying out image based on described data of blocking comprises:

The described data of back projection are with the Density Distribution in the middle of generating; And

To the object function filtering of described centre, to create the quite accurate image of described area-of-interest.

Images