WO2007004196A2

WO2007004196A2 - Exact fbp type algorithm for arbitrary trajectories

Info

Publication number: WO2007004196A2
Application number: PCT/IB2006/052248
Authority: WO
Inventors: Thomas Köhler; Claas Bontus; Roland Proksa
Original assignee: Philips Intellectual Property & Standards Gmbh; Koninklijke Philips Electronics N. V.
Priority date: 2005-07-05
Filing date: 2006-07-04
Publication date: 2007-01-11
Also published as: WO2007004196A3

Abstract

Exact methods of FBP reconstruction may have the restriction that the object point to be reconstructed and the first and last source position used for back- projection must lie on a line. According to an exemplary embodiment of the present invention, a method of FBP reconstruction is provided, comprising a filtering of the projection data along a projected M-line and a back-projecting of the filtered projection data over an interval larger than the PI interval of the object point. This may provide for an exact FBP type algorithm for arbitrary trajectories.

Description

Exact FBP type algorithm for arbitrary trajectories

The present invention relates to the field of X-ray imaging. In particular, the present invention relates to a computer tomography apparatus for examination an object of interest, to a method of examining an object of interest, an image processing device, a computer-readable medium and a program element. Exact reconstruction algorithms for cone-beam computed tomography

(CT) are of the type filtered-back projection (FBP) or back-projection filtering (BPF). Usually, exact reconstruction can be performed, if the object point to be reconstructed and the first and last source position used for back-projection lie on a line, for example the PI line of the object point. Furthermore, Pack et al. presented a BPF style method for arbitrary (complete) trajectories that does not fall under this restriction, which is called Pack method or Pack reconstruction in the following and described in Pack, Noo, and Clackdoyle, IEEE Trans. Med. Imag., 24 (1), Jan 2005, pp. 70-85, which is hereby incorporated by reference.

For reasons of dose utilization, the afore-mentioned restriction of the back-projection interval is highly unwanted. Furthermore, the BPF style may prohibit a region of interest reconstruction.

It may be desirable to provide for an improved exact FBP reconstruction. According to an exemplary embodiment of the present invention, a computer tomography apparatus for examination of an object of interest may be provided, the computer tomography apparatus comprising a radiation source adapted for moving along a source path and for emitting electromagnetic radiation, and a reconstruction unit, the reconstruction unit being adapted for differentiating projection data, filtering the projection data along a part of finite length of a first projected line, the line connecting the source path and an object point to be reconstructed, and wherein the part is limited by the projection of two points on the line, which are outside the object of interest (107), and back-projecting the filtered projection data over an interval comprising a PI interval of the object point. Thus, according to this exemplary embodiment of the present invention, a M-line reconstruction may be performed which uses redundancies in projection data. Furthermore, the reconstruction is a FBP style reconstruction.

According to another exemplary embodiment of the present invention, the interval over which the filtered projection data is back-projected ranges from min(λ₀, λs) to max(λ₀, λE), wherein λ₀ is a source angle at which the line connecting the source path and the object point to be reconstructed intersects the source path, λs is a start point of the PI interval of the object point and λE is an end point of the PI interval of the object point. Therefore, according to this exemplary embodiment of the present invention, the interval over which the filtered projection data is back-projected comprises both the M-line and the Pi-line. The filter direction is defined by the M-line.

According to another exemplary embodiment of the present invention,

According to another exemplary embodiment of the present invention, the reconstruction unit is further adapted for differentiating the projection data on the basis of a Katsevich reconstruction scheme.

The differentiation may be performed along parallel rays from different source positions. This is in particular beneficial if a so-called focus-centred detector is used because in this case, any interpolation in axial direction is avoided.

According to another exemplary embodiment of the present invention, a reconstruction of the first projected line results in first reconstruction data, wherein the reconstruction unit is further adapted for reconstructing a second projected line connecting the source path and the object point to be reconstructed, resulting in a second reconstruction data, and performing a weighted average of the second reconstruction data and the first reconstruction data.

Therefore, a signal-to-noise ratio may be optimized by reconstruction of several M-lines passing through the object point and perform a weighted average of the results. According to another exemplary embodiment of the present invention, the filtering is a Hubert filtering. The computer tomography apparatus may comprise an electromagnetic radiation source adapted for emitting electromagnetic radiation to the object of interest and a collimator arranged between the electromagnetic radiation source and the detecting elements, wherein the collimator is adapted for collimating an electromagnetic radiation beam emitted by the electromagnetic radiation source to form a cone-beam.

The computer tomography apparatus according to the invention may be applied as a baggage inspection apparatus, a medical application apparatus, a material testing apparatus or a material science analysis apparatus. A field of application of the invention may be baggage inspection, since the defined functionality of the invention allows a secure and reliable analysis of the content of a baggage item allowing to detect suspicious content.

Such an apparatus or method in accordance with an exemplary embodiment of the present invention may create a high quality automatic system that may automatically recognize certain types of materials and, if desired, trigger an alarm in the presence of dangerous materials.

According to another exemplary embodiment of the present invention, a method of examining an object of interest with a computer tomography apparatus may be provided, the method comprising the steps of differentiating projection data, filtering the projection data along a first projected line, the line connecting a source path of a radiation source and an object point to be reconstructed, and back-projecting the filtered projection data over an interval comprising a PI interval of the object point. It is believed that this may allow for an improved exact FBP reconstruction. According to another exemplary embodiment of the present invention, an image processing device for examining an object of interest with a computer tomography apparatus may be provided, the image processing device comprising a memory for storing projection data and a reconstruction unit adapted for carrying out the above-mentioned method steps. According to another exemplary embodiment of the present invention, a computer-readable medium may be provided, in which a computer program of examining an object of interest with a computer tomography apparatus is stored which, when being executed by a processor, is adapted to carry out the above-mentioned method steps.

The present invention also relates to a program element of examining an object of interest, which, when being executed by a processor, is adapted to carry out the above-mentioned method steps. The program element may be stored on the computer-readable medium and may be loaded into working memories of a data processor. The data processor may thus be equipped to carry out exemplary embodiments of the methods of the present invention. The computer program may be written in any suitable programming language, such as, for example, C++ and may be stored on a CD-ROM. Also, the computer program may be available from a network, such as the Worldwide Web, from which it may be downloaded into image processing units or processors, or any suitable computers.

It may be seen as the gist of an exemplary embodiment of the present invention, that a M-line reconstruction is performed using redundancies in the projection data. The filtering of the differentiated projection data may be performed along projected M-lines. After that, a back-projection may be performed over an interval which is larger and comprises the Pi-interval of the object point.

These and other aspects of the present invention will become apparent from and elucidated with reference to the embodiment described hereinafter. Exemplary embodiments of the present invention will be described in the following, with reference to the following drawings.

Fig. 1 shows a simplified schematic representation of a CT scanner system according to an exemplary embodiment of the present invention.

Fig. 2 shows a schematic representation of a filter direction according to an exemplary embodiment of the present invention.

Fig. 3 shows a schematic representation of the detector weighting function w for the example of a helical acquisition. Fig. 4 shows a schematic representation of the location of the Pi-line of the voxel and the M-line according to an exemplary embodiment of the present invention. Fig. 5 shows an exemplary embodiment of an image processing device according to the present invention, for executing an exemplary embodiment of a method in accordance with the present invention.

Fig. 6 shows a schematic representation of back-projection intervals according to an exemplary embodiment of the present invention.

Fig. 7 shows a flow-chart of an exemplary embodiment of a method of examination of an object of interest according to the present invention.

Fig. 8 shows a flow-chart representing an exemplary embodiment of an examination of an object of interest according to an exemplary embodiment of the present invention.

Fig. 9 shows an exemplary embodiment of an acquisition geometry according to an exemplary embodiment of the present invention.

The illustration in the drawings is schematically. In different drawings, similar or identical elements may be provided with the same reference numerals.

Fig. 1 shows an exemplary embodiment of a CT scanner system according to an exemplary embodiment of the present invention. With reference to this exemplary embodiment, the present invention will be described for the application in medical imaging. However, it should be noted that the present invention is not limited to this application, but may also be applied in the field of baggage inspection, or other industrial applications, such as material testing.

The computer tomography apparatus 100 depicted in Fig. 1 is a cone- beam CT scanner. The CT scanner depicted in Fig. 1 comprises a gantry 101, which is rotatable around a rotational axis 102. The gantry 101 is driven by means of a motor 103. Reference numeral 104 designates a source of radiation such as an X-ray source, which, according to an aspect of the present invention, emits a polychromatic radiation.

Reference numeral 105 designates an aperture system which forms the radiation beam emitted from the radiation source to a cone-shaped radiation beam 106. The cone-beam 106 is directed such that it penetrates an object of interest 107 arranged in the centre of the gantry 101, i.e. in an examination region of the CT scanner, and impinges onto the detector 108. As may be taken from Fig. 1, the detector 108 is arranged on the gantry 101 opposite to the source of radiation 104, such that the surface of the detector 108 is covered by the cone-beam 106. The detector 108, which is depicted in Fig. 1, comprises a plurality of detector elements 123 each capable of detecting, in an energy-resolving manner X-rays or individual photons which have penetrated the obj ect of interest 107.

During a scan of the object of interest 107, the source of radiation 104, the aperture system 105 and the detector 108 are rotated along the gantry 101 in the direction indicated by arrow 116. For rotation of the gantry 101 with the source of radiation 104, the aperture system 105 and the detector 108, the motor 103 is connected to a motor control unit 117, which is connected to a calculation or determination unit 118.

In Fig. 1, the object of interest 107 may be a patient or an item of baggage which is disposed on a conveyor belt 119. During the scan of the object of interest 107, while the gantry 101 rotates around the item of baggage 107, the conveyor belt 119 displaces the object of interest 107 along a direction parallel to the rotational axis 102 of the gantry 101. By this, the object of interest 107 is scanned along a helical scan path. The conveyor belt 119 may also be stopped during the scans to thereby measure single slices. Instead of providing a conveyor belt 119, for example, in medical applications where the object of interest 107 is a patient, a movable table may be used. However, it should be noted that in all of the described cases it may also be possible to perform other scan pathes such as the saddle trajectory by moving the table periodically back and forth at twice the frequency of the source-detector arrangement.

The detector 108 may be connected to the calculation unit 118. The calculation unit 118 may receive the detection result, i.e. the read-outs from the detector elements 123 of the detector 108 and may determine a scanning result on the basis of the read-outs. Furthermore, the calculation unit 118 communicates with the motor control unit 117 in order to coordinate the movement of the gantry 101 with motors 103 and 120 with the conveyor belt 119.

The calculation unit 118 may be adapted for constructing an image from read-outs of the detector 108 by differentiating projection data, filtering the projection data along an M-line, and back-projecting the filtered projection data over an interval comprising a PI interval of the object point, according to an exemplary embodiment of the present invention. A reconstructed image generated by the reconstruction unit 118 may be output to a display (not shown in Fig. 1) via an interface 122.

The calculation unit 118 may be realized by a data processor to process read-outs from the detector elements 123 of the detector 108. Furthermore, as may be taken from Fig. 1 , the reconstruction unit 118 may be connected to a loudspeaker 121, for example, to automatically output an alarm in case of the detection of suspicious material in the item of baggage 107.

The computer tomography apparatus 100 for examination of the object of interest 107 includes the detector 108 having the plurality of detecting elements 123 arranged in a matrix-like manner, each being adapted to detect X-rays. Furthermore, the computer tomography apparatus 100 comprises the determination unit or reconstruction unit 118 adapted for reconstructing an image of the object of interest 107.

The computer tomography apparatus 100 comprises the X-ray source 104 adapted to emit X-rays to the object of interest 107. The collimator 105 provided between the electromagnetic radiation source 104 and the detecting elements 123 is adapted to collimate an electromagnetic radiation beam emitted from the electromagnetic radiation source 104 to form a cone-beam. The detecting elements 123 form a multi-slice detector array 108. The computer tomography apparatus 100 may be configured as a medical imaging apparatus or baggage inspection apparatus. Fig. 2 shows a schematic representation of the filter direction for the exact FBP type algorithm for the exemplary case of a PI+ acquisition. Here, PI+ refers to an acquisition of data using a helical trajectory, which allows to do an exact PI reconstruction, but also some additional data outside the PI window is acquired. It should be noted that signal-to-noise may be optimized by reconstruction of several M- lines passing through the object point and performing a weighted average of the results. The dots depicted in Fig. 2, such as dots 201, 202, represent the object point 301 of Fig. 4 projected onto the detector from several source positions. The respective filter direction is indicated by the lines through the object point, such as lines 203, 204. The filter direction corresponds to the projected M-line. All object points on the M-line may share the same filter lines.

In other words, Fig. 2 depicts an illustration of an application of an exemplary method of the invention to a helical trajectory. The projected position of the object point 301 in Fig. 4 is shown for several source positions between /I₃ and A₂.

Additionally, the filter lines are shown. Note that the filtering is performed along these lines on finite length. In contrast, the exact BPF method of the pack method would require filtering along the same direction, but the lines are of infinite length. According to an aspect of the present invention, the M-line reconstruction as suggested in the BPF reconstruction scheme by Pack et al. is adapted to the FBP style reconstruction. The reconstruction scheme according to an exemplary embodiment of the present invention and which is performed by the reconstruction unit 118 comprises the following steps: 1. Differentiation of the projection data as in Katsevich style reconstruction. For example, the differentiation may be performed along parallel rays from different source positions. However, it should be noted that other differentiation techniques for differentiating the projection data may be performed, as for instance disclosed in the embodiment 2. Filtering of the differentiated data along projected M-lines, such as, for example, Hubert filtering. An M-line is a line connecting the source path and the object point to be reconstructed. The source angle where the M-line intersects the trajectory is denoted as λo.

3. Back-projection over the interval from min(λ₀, λs) to max(λ₀, λE), where λs and λE denote the start and end point of a PI interval of the object point.

Therefore, according to an exemplary embodiment of the present invention, an M-line reconstruction is performed using redundancies in the projection data. First a differentiation of the projection data is performed, followed by a filtering step along projected M-lines. Then, a back-projection is performed over an interval which may be bigger than the PI interval and comprises the PI interval.

In the following, an exemplary embodiment of a method according to the present invention is described in greater detail:

In general, the notation as used by Pack et al is followed, as described in the above-cited Pack reference. The x-ray source moves on a curve a{λ) . We assume to have a planar detector. Detector values are parameterized by the two coordinates u and v. Exact FBP formulation without redundant data usage:

Let Θ₁₂ be a unit vector pointing from source position a{\) to a{λ₂) .

Without loss of generality, we assume

and λ₂ are referred to as λs and λE and that λ₃ is referred to as λ₀. Let

The following relations hold true (see Eqn. (48), (36), and (24) of the above-cited Pack reference)

I [ D\ fi \λ ι gi {X u"(λ f(f\\, t ^*{X, r;t >\\ dλ \ C ( ^

[S[X) - Ht⁾) - c_tt

where u*(λ,r(t)) and v*(λ,r(t)) are the u- and v-coordinate of the projection of r{t) onto the detector from source position λ and g_F are the measured line integrals of the object function /differentiated along ά\λ) . The constant C can be computed according to Eq. (12) or (13) of the Pack reference. Let

IU) - hftf)) >5) be the value of the object function on the Pi-line. From the Pack reference (Eq. (8)), we know that the truncated inverse Hubert transform has the solution

with E being a constant. The integration limits are selected such, that it is known that^(t) = 0 for t ≤ t_x and t ≥ t₂. Inserting Eq. (4) in Eq. (6) yields

ft/')) < ^* ι A ?V ^ , , „,

with

Switching the order of integration yields

Note that the integration over t' is now carried out in projection space.

Another important point is that the integration is performed along straight lines on a planar detector, since both, u* and v*, linearly on f in this geometry. The end points for the t' integration are then given by the projection of P(Y₁) and P(Y₂) onto the detector. If applied to a helical trajectory, Eq. (11) can be seen as an alternative formulation of the exact FBP type algorithm described by Sidky, Zou, and Pan, Minimum data image reconstruction algorithms with shift-invariant filtering for helical, cone-beam CT. Phys. Med. BwL, 50:1643 - 1657, 2005.

Exact FBP formulation with redundant data usage: Consider now the case that we want to use redundant data. Let us start from Eq. (38) in the Pack reference. Remember A₁ and A₂ correspond to the source positions of a Pi-line of r(t) :

where C is again a constant and S(A₃, F(Y)) is a unit vector pointing from 0(/I₃) to r(t) . In the case of redundant data usage, we have either A₃ < A₁ or X₃ > A₂. We will discuss the case of X₃ < A₁ and the other case can be handled accordingly. Let now rij) - S[X₃) - i3{X_{3 *} τ\t\) , ( 13)

Again, we need some values t\ and h such, it is know that^(t) = 0 for t < t_j and t ≥ t₂. Then we have

- bifζttΛiΛoy + C (U)

( 13)

- S- C 1 16}

where we introduced an angular weighting function w(λ) in the last step with respect to

tr{λ) ~~ I 1 Λi <s A s Aj ( 17⁾

[ 0 o??c.

This last step can be made because [X₃ ; X_x ] c: \λ₃ ; A₂ ] . Now it is important to note that in the case of redundant data usage, A₁ and A₂ depend on t, which was not the case in the simple case of no redundant data usage because ώ(λ₃, r(t)) is no longer pointing along a Pi-line. Inserting Eq. (16) into Eq. (6), we obtain )

Here, we made the dependence of A₂ and w (through A₁ ) explicit. In contrast to the case of no redundant data usage, the limits of the inner integral depend on the integration variable in the outer integral, so we cannot switch orders directly. The key point that allows a the change of order is the following: If the source reaches , the object point r{t) is projected onto the same point of the detector as the opposing source position a(A₂ (Y)) ■ In other words, A₂ (t) and w(t, A) can be mapped statically onto the detector area. We will illustrate this for the case of a high-pitch helical acquisition. The projection of the source path onto the detector follows the lines (see e.g. Eqn. (8) and (9) in R. Proksa, Th. Kόhler, M. Grass, and J. Timmer. The n-PI- method for helical cone-beam CT. /EEE Trans. Med. Imag., 19(9):848 - 863, 2000).

^<<- iu⁾ - ^^p [ ^{1 ^} Jr) (^ ^Λτc{m jj ) - ^{-^Oi

where P is the table travel per rotation, R is the source radius. Assuming a positive pitch (P>0), v⁺(u) defines the projection of the source path in the future, while v- (u) defines the projection of the source path in the past. Thus, the following weighting function on the differentiated projection data g_F

can be used to avoid the dependencies of A₂ and w on t' . See Fig. 3 for an illustration. Using this weighting, we can proceed with /(') m)

_\Λ< κ)(h t) v n\ ά^>

\{a(X) ~ rt t' h v->

L t 2JT>

where the explicit dependence of w, w*, and v* on λ and r(t') has been omitted for the sake of compactness. Furthermore, the source angle A₄ has been additionally introduced which is subject to the inequation

The geometry for this exemplary embodiment is shown in Fig. 4, the resulting filter lines are shown in Fig. 2.

Fig. 4 shows a illustration of an application of an exemplary method according to the present invention to a helical trajectory. The source path 206 from A₃ to A₂ is drawn thick. The M-line where reconstruction should be performed is indicated by reference numeral 203. Additionally, the object point on the M-line is indicated by reference numeral 301. The Pi-line of this particular object point is indicated by reference numeral 205. Finally, the two black points 207, 208 indicate the limits of the truncated inverse Hilbert-transform F(Y₁) and F(Y₂) . Fig. 5 depicts an exemplary embodiment of an image processing device according to the present invention for executing an exemplary embodiment of the method in accordance with the present invention. The image processing device 400 depicted in Fig. 5 comprises a central processing unit (CPU) or image processor 401 connected to a memory 402 for storing an image depicting an object of interest, such as a patient or an item of baggage. The data processor 401 may be connected to a plurality of input/output network for diagnosis devices, such as a CT device. The data processor 401 may furthermore be connected to a display device 403, for example, a computer monitor, for displaying information or an image computed or adapted in the data processor 401. An operator or user may interact with the data processor 401 via a keyboard 404 and/or other output devices, which are not depicted in Fig. 5.

The examination of an object of interest according to the present invention may allow for an exact FBP type reconstruction of for arbitrary trajectories. The currently used cone-beam reconstruction algorithms for helical trajectories are approximated and suffer from cone-beam artefacts. These artefacts can be avoided by so-called exact reconstruction methods. These exact methods are an exact analytical inversion. Exact algorithms may suffer from two drawbacks. The first drawback is, that, until recently, these methods cannot use redundant data. Recently, a new method has been published that allows the use of redundant data. This method will be called the Pack method or Pack reconstruction in the following and is described in J.P. Pack, F. Noo, R. Clackdoyle, "Cone-Beam Reconstruction Using the Back- Projection of Locally Filtered Projections", IEEE Transaction on Medical Imaging, Vol. 24, No 1, Jan 2005, pp. 70-85, which is hereby incorporated by reference. The Pack method solves the dose utilization part because it uses all measured data. However, the Pack method may still suffer from motion sensitivity because it may not support a smooth transition of the overscan data utilization at the detector border.

It may be desirable to provide for an improved exact BPF reconstruction. According to an exemplary embodiment of the present invention, a computer tomography apparatus for examination of an object of interest may be provided, the computer tomography apparatus comprising a radiation source emitting an electromagnetic radiation beam, and a reconstruction unit, the reconstruction unit being adapted for performing a first projection data reconstruction on a first set of M- lines, the first set of M-lines corresponding to a first overscan parameter, the first reconstruction resulting in a first image, and performing a second projection data reconstruction on a second set of M-lines, the second set of M-lines corresponding to a second overscan parameter, the second reconstruction resulting in a second image. The first reconstruction uses a first projection surface and the second reconstruction uses a second projection surface, wherein the first overscan parameter corresponds to a first distance between the first projection surface and a surface of the beam, and wherein the second overscan parameter corresponds to a second distance between the second projection surface and the surface of the beam.

In this context, an M-line is a line connecting the source path of a radiation source of the computer tomography apparatus and an object point to be reconstructed, the object point being part of the object of interest.

The beam of the computer tomography apparatus may, according to an exemplary embodiment of the present invention, be collimated to restrict the beam to a sensitiv detector area. The surfaces of the resulting beam are called beam surface.

The reconstruction, which, according to an exemplary embodiment of the present invention, may be a Pack reconstruction, may be done on M-Lines. A set of M- Lines defines a plain that is called M-Line surface. These M-Line surfaces define one border of the effectively used part of the x-ray beam. If an M-Line surface is identical to the beam surface, the related reconstruction uses all data of the related side of the beam. If the M-Line surface is inside the beam, away from the beam surface, the related reconstruction uses only parts of the measured data.

A plurality of projection data reconstructions may be performed, each on a respective set of M-lines. This may provide for an exact reconstruction method using all redundant data of a helical cone-beam acquisition with arbitrary pitch. Furthermore, a smooth transition of the utilization of redundant data at the detector borders may be provided.

According to another exemplary embodiment of the present invention, the reconstruction unit is further adapted for adding the first image and the second image and dividing the resulting image by a factor corresponding to the overall number of images added. Therefore, by adding all images, the data contribution may grow along the M-line references toward the centre of the projection in a staircase shaped function. If the overall number of images added is large enough, the utilization may become smooth and may mitigate the motion sensitivity of the reconstruction unit.

According to another exemplary embodiment of the present invention, the reconstruction unit is further adapted for weighting of the projection data and differentiating the projection data before the first and second projection data reconstructions. According to another exemplary embodiment of the present invention, the reconstruction unit is further adapted for performing a fan-to-parallel rebinning of the projection data before the first and second projection data reconstructions.

According to another exemplary embodiment of the present invention, the first and the second reconstructions are Pack reconstructions.

Thus, according to this exemplary embodiment of the present invention, the Pack method may be improved.

According to another exemplary embodiment of the present invention, the reconstruction unit is further adapted for performing a third projection data reconstruction on a third set of M-lines, the third set of M-lines corresponding to a third overscan parameter, the third reconstruction resulting in a third image, and performing a fourth projection data reconstruction on a fourth set of M-lines, the fourth set of M-lines corresponding to a fourth overscan parameter, the fourth reconstruction resulting in a fourth image. Hereby, the third reconstruction uses a third projection surface and the fourth reconstruction uses a fourth projection surface, wherein the third overscan parameter corresponds to a third distance between the third projection surface and the surface of the beam, and wherein the fourth overscan parameter corresponds to a fourth distance between the fourth projection surface and the surface of the beam. The third and the fourth distances are bigger than the first and the second distances. Therefore, a plurality of different Pack reconstructions on M-lines may be performed, wherein each pair of M-lines may have different overscan parameters.

According to another exemplary embodiment of the present invention, the first distance equals the second distance and the third distance equals the fourth distance. Therefore, the first set of M-lines and the second set of M-lines have the same overscan parameter and the third and the fourth sets of M-lines have another same overscan parameter.

According to another exemplary embodiment of the present invention, the first projection surface corresponds to an upper projection surface and the second projection surface corresponds to a lower projection surface.

Thus, the first and second overscan parameter (which may equal each other) may define the outermost detector row as reference for the M-lines. With increasing overscan parameter, the reference detector row may move from the real detector border towards the centre of the detector. It should be noted, however, that other non-linear or curved virtual borders may be used.

According to another exemplary embodiment of the present invention, the computer tomography apparatus further comprises a collimator arranged between the electromagnetic radiation source and detecting elements, wherein the collimator is adapted for collimating an electromagnetic radiation beam emitted by the electromagnetic radiation source to form a cone-beam.

The computer tomography apparatus according to the invention may be applied as a baggage inspection apparatus, a medical application apparatus, a material testing apparatus or a material science analysis apparatus. A field of application of the invention may be baggage inspection, since the defined functionality of the invention allows a secure and reliable analysis of the content of a baggage item allowing to detect suspicious content, even allowing to determine the type of a material inside such a baggage item.

Such an apparatus or method in accordance with an exemplary embodiment of the present invention may create a high quality automatic system that may automatically recognize certain types of materials and, if desired, trigger an alarm in the presence of dangerous materials. According to another exemplary embodiment of the present invention, a method of examining an object of interest with a computer tomography apparatus may be provided, the method comprising the steps of performing a first projection data reconstruction on a first set of M-lines, the first set of M-lines corresponding to a first overscan parameter, the first reconstruction resulting in a first image, and performing a second projection data reconstruction on a second set of M-lines, the second set of M- lines corresponding to a second overscan parameter, the second reconstruction resulting in a second image. The first reconstruction uses a first projection surface and the second reconstruction uses a second projection surface, wherein the first overscan parameter corresponds to a first distance between the first projection surface and the surface of the beam and wherein the second overscan parameter corresponds to a second distance between the second projection surface and the surface of the beam. It is believed that this may allow for an improved exact BPF reconstruction.

According to another exemplary embodiment of the present invention, an image processing device for examining an object of interest with a computer tomography apparatus may be provided, the image processing device comprising a memory for storing projection data and a reconstruction unit adapted for carrying out the above-mentioned method steps.

According to another exemplary embodiment of the present invention, a computer-readable medium may be provided, in which a computer program of examining an object of interest with a computer tomography apparatus is stored which, when being executed by a processor, is adapted to carry out the above-mentioned method steps.

According to an aspect of the present invention, a reconstruction is performed using redundant data of a helical cone-beam acquisition with arbitrary pitch. According to an exemplary embodiment of the present invention, multiple projection data reconstructions are performed on a plurality of M-lines, after which the resulting images are added and divided by the number of added images. This may support a smooth transition of the utilization of redundant data at the detector borders.

Fig. 6 shows a schematic representation of back-projection intervals according to an exemplary embodiment of the present invention. Fig. 6 shows a source trajectory 203 being of helical shape along which an electromagnetic radiation source (which is not depicted in Fig. 2) moves. The radiation source moves along the helical path 203 around the object point 201 which is part of the object of interest.

The PI interval of the object point 201 corresponds to the segment 208 along the helix 203. The PI interval corresponds to the minimum back-projection interval Ω(n).

The two back-projection intervals with maximal overscan Ω(l) are indicated by the dash-dotted lines 204, 205. Back-projection intervals with intermediate overscan Ω(j) are indicated by the dashed lines 206, 207. Fig. 7 shows a flow-chart of an exemplary embodiment of a method of examination of an object of interest according to an exemplary embodiment of the present invention. The method starts with step 1 by performing a weighting of the measured projections. Then, in step 2, an optional fan-to-parallel rebinning of the measured projections may be performed, after which, in step 3, the derivative of the rebinned data is calculated.

In case of the optional fan-to-parallel rebinning of the measured projections, the following differentiation may be performed in a Katsevich style in which the differentiation may be performed along parallel rays from different source positions.

Then, in step 4, two separate Pack reconstructions of M-lines may be performed. Hereby, the M-lines are defined relative to the surface of the projection. The two reconstructions differ only in that one reconstruction uses the upper projection surface while the other uses the lower projection surface.

This first two separate Pack reconstructions are performed on M-lines corresponding to the same overscan parameter Ω(l) defining a maximum overscan.

The overscan parameter Ω(i) defines how far away the M-lines are from the projection surface. For i = 1, Ω(i) should be such that the projection surface defines the M-lines. Ω(i) may grow with growing i.

One particular implementation of Ω(i) may be defined such that for i = 1, Ω(i) defines the outermost detector row as reference for the M-lines. With increasing i, the reference detector row moves from the real detector border towards the center. However, other non-linear or curved virtual borders may be used.

Step 4 may be repeated with a different overscan parameter Ω(2). Now, the respective M-lines are farther away from the projection surface (since i has increased). After having performed two further separate Pack reconstructions on the new M-lines, step 4 may be repeated with a third overscan parameter Ω(3). Here, the distance between the respective M-lines and the projection surface is even bigger compared to the distance corresponding to Ω(l) and Ω(2).

Step 4 may be further repeated with different overscan parameters defining different M-lines.

After that, in step 5, all reconstructed images are added and divided by 2n, where n represents the number of overscan parameters used (which corresponds to the number of repetitions of step 4). Then, in step 6, the resulting data may be resampled from an M-line grid to another representation, such as, for example, a Cartesian grid.

It should be noted, however, that step 2 is optional. The M-line definition as well as the Pack-reconstruction may be performed on cone-beam projections or parallel rebinned so-called wedges.

The effect of this method may be understood by studying the impact of detector areas to the reconstruction. For example, the outermost detector part, that is used only for i = 1, has a contribution proportional to l/2n. The next part that is used for i = 1 and i = 2 has contribution proportional to 2/2n. The inner part has contribution 2n/2n = l.

Considering all n reconstructions, the data contribution may grow along the M-line references toward the center of the projection in a staircase shaped function. If n is large enough, the utilization may become smooth and may mitigate the motion sensitivity of the reconstruction. Exact reconstruction algorithms for cone-beam computed tomography

(CT) are currently all of the type filtered back-projection (FBP) or back-projection filtering (BPF). Usually, exact reconstruction can be performed, if the object point to be reconstructed and the first and last source position used for back-projection lie on a line, for example, the PI line of the object point. Furthermore, PACK et al. presented a BPF style method for arbitrary (complete) trajectories that does not fall under this restriction (J. Pack, F. Noo, and R. Clackdoyle, IEEE Trans. Med. Imag., 24 (1), Jan 2005, pp. 70- 85, which is hereby incorporated by reference).

However, there is an object point dependent magnification factor in the denominator of the back-projection part of the BPF method by Pack which may prohibit an efficient implementation of the back-projection in hardware.

It may be desirable to provide for an improved exact reconstruction for CT.

According to an exemplary embodiment of the present invention, an examination apparatus for examination of an object of interest may be provided, the examination apparatus comprising a source adapted for moving along a source path and a reconstruction unit, the reconstruction unit being adapted for differentiating projection data along parallel rays from different source positions, wherein the differentiation results in an elimination of a square in an object point dependent magnification factor of a back-projection part of a reconstruction scheme.

Therefore, according to this exemplary embodiment of the present invention, a differentiation of an acquired projection data is no longer performed in cone-beam geometry but in a parallel geometry. Since this may eliminate a square in the denominator of the back-projection part of the reconstruction scheme, hardware implementation of the back-projection scheme may be facilitated.

According to another exemplary embodiment of the present invention, the reconstruction unit is further adapted for back-projecting the differentiated projection data, wherein the back-projection comprises a re-binning of the differentiated projection data into parallel geometry.

Therefore, the back-projection may be performed in parallel geometry (like the differentiating step before). This may eliminate the object point dependent magnification factor in the back-projection part of the reconstruction scheme, therefore providing for an efficient implementation of the back-projection in hardware.

According to another exemplary embodiment of the present invention, the reconstruction unit is further adapted for weighting the re-binned differentiated projection data, ensuring that the exactness of the algorithm is preserved.

According to another exemplary embodiment of the present invention, the reconstruction scheme is an exact back-projection filtering cone-beam reconstruction on the basis of a Pack reconstruction.

Thus, arbitrary and complete trajectories may be used for reconstruction of the images.

The examination apparatus may comprise an electromagnetic radiation source adapted for moving along a helical source path and for emitting electromagnetic radiation to the object of interest. Furthermore, the CT apparatus may comprise a collimator arranged between the electromagnetic radiation source and detecting elements, wherein the collimator is adapted for collimating an electromagnetic radiation beam emitted by the electromagnetic radiation source to form a cone-beam. The examination apparatus according to the invention may be applied as a baggage inspection apparatus, a medical application apparatus, a material testing apparatus or a material science analysis apparatus. A field of application of the invention may be baggage inspection, since the defined functionality allows a secure and reliable analysis of the content of a baggage item allowing to detect suspicious content, even allowing to determine the type of a material inside such a baggage item.

According to another exemplary embodiment of the present invention, the examination apparatus may be selected from the group consisting of CT (computed tomography) imaging system, CSCT (coherent scatter computed tomography) imaging system, PET (positron emission tomography) imaging system, and SPECT (single photon emission computerized tomography) imaging system.

According to another exemplary embodiment of the present invention, a method of examining an object of interest with an examination apparatus may be provided, the method comprising the step of differentiating projection data along parallel rays from different source positions, wherein the differentiation results in an elimination of a square in an object point dependent magnification factor of a back- projection part of a reconstruction scheme.

This may provide for an improved exact reconstruction for computer tomography and may allow for an efficient implementation of the back-projection in hardware.

According to another exemplary embodiment of the present invention, the method further comprises the steps of back-projecting the differentiated projection data and weighting the re-binned differentiated projection data, resulting in an elimination of the object point dependent magnification factor in the back-projection part of the reconstruction scheme. Hereby, the back-projection comprises a re-binning of the differentiated projection data into parallel geometry.

Thus, according to this exemplary embodiment of the present invention, the differentiation of the projection data is performed in a parallel geometry and the back-projecting of the differentiated projection data is performed in a parallel-geometry as well. Thus, the object point dependent factor in the back-projection scheme may be eliminated.

According to another exemplary embodiment of the present invention, an image processing device for examining an object of interest with an examination apparatus may be provided, the image processing device comprising a memory for storing projection data and a reconstruction unit adapted for carrying out the above- mentioned method steps.

According to another exemplary embodiment of the present invention, a computer-readable medium may be provided, in which a computer program of examining an object of interest with an examination apparatus is stored which, when being executed by a processor, is adapted to carry out the above-mentioned steps.

According to an aspect of the present invention, that an exact BPF type cone-beam CT reconstruction is provided which can be used for arbitrary trajectories. According to an exemplary embodiment of the present invention, the differentiation is performed along parallel rays and the pre-processed data is re-binned into parallel geometry. This may eliminate the object point dependent factor in the back-projection part of the reconstruction scheme.

Fig. 8 shows a flow-chart of an exemplary embodiment of a method according to the present invention. The method starts at step 1 by the acquisition of projection data. This acquisition may be performed by a source of electromagnetic radiation emitting a radiation beam penetrating the object of interest and a detector comprising a plurality of detecting elements adapted for detecting the electromagnetic radiation. The detected signals may then be stored in a storage medium or memory for later processing steps or may be directly further processed without intermediate storing. The further processing may be performed by a reconstruction unit.

The reconstruction method according to an exemplary embodiment of the present invention may be performed on the basis of the above referenced Pack reconstruction scheme, in which the back-projection part of the BPF method is

where x is the object point to be reconstructed, ^,A₂ are start and end- point of the back-projection interval (where at least one of A₁ or A₂ is the end point of a PI, ft-PI, or generalized PI line), g_F are the line integrals differentiated in cone-beam geometry along the projected path a of the source at A , D is the distance from the source to the detector, and e_w is the normal vector of the detector plane. Finally, u(A,x) and v(A,x) are the coordinates of the object point x projected onto the detector from the source position A . The object point dependent magnification factor

the denominator may prohibit an efficient implementation of the back-projection in hardware. In order to eliminate the object point dependent denominator and the back-projection, two modifications of the Pack procedure may be performed according to an exemplary embodiment of the present invention. The first modification may affect the differentiation step. Instead of differentiation in cone-beam geometry, the differentiation is performed along parallel rays from different source positions like in the exact filtered back-projection type algorithms, which are described e.g. in C.Bontus, et.al., MedPhys. vol.30(9), pp.2493-2502, which is hereby incorporated by reference. The differentiation is performed in step 2. This modification may eliminate the square in the denominator.

The second modification takes place in steps 3 and 4 and is part of the back-projection. By re-binning the pre-processed data into parallel geometry (step 3) and application of proper weighting of the re-binned differentiated projection data, the remaining object point dependent factor is removed. Here, the weighting may be applied such that the exactness of the algorithm is preserved.

The rebinning into parallel geometry in step 3 may be applied as follows. A parallel detector is a virtual detector, which contains data taken from different source positions (as indicated by reference numerals 301 - 307 in Fig.9). Data corresponding to one particular column of the parallel detector is associated with certain rays. As illustrated in Fig.9, these rays form a fan. The name of the parallel detector results from the fact that for different columns the different fans are parallel. The so-called Wedge detector is a special case of a parallel detector. Here, data associated with one particular row of the Wedge detector are all extracted from data of one particular row of the focus-centred detector but from different source positions. Using Wedge geometry for the back-projection reduces the number of interpolations and, therefore, results in a good spatial resolution.

Exemplary embodiments of the invention may be sold as a software option to CT scanner console, imaging work stations or PACS work stations.

It should be noted that the term "comprising" does not exclude other elements or steps and the "a" or "an" does not exclude a plurality and that a single processor or system may fulfill the functions of several means or units recited in the claims. Also elements described in association with different embodiments may be combined.

It should also be noted, that any reference signs in the claims shall not be construed as limiting the scope of claims.

Claims

CLAIMS:

1. A computer tomography apparatus (100) for examination of an object of interest (107), the computer tomography apparatus (100) comprising: a radiation source (104) adapted for moving along a source path and for emitting electromagnetic radiation; a reconstruction unit (118), the reconstruction unit being adapted for: differentiating projection data; filtering the projection data along a part of finite length of a first projected line, the line connecting the source path and an object point to be reconstructed, and wherein the part is limited by the projection of two points on the line, which are outside the object of interest (107); and back-projecting the filtered projection data over an interval comprising a PI interval of the object point.

2. The computer tomography apparatus ( 100) of claim 1 , wherein the interval over which the filtered projection data is back- projected ranges from min(λ₀, λs) to max(λ₀, λE); wherein λ₀ is a source angle at which the line connecting the source path and the object point to be reconstructed intersects the source path; wherein λs is a start point of the PI interval of the object point; and wherein X_E is an end point of the PI interval of the object point.

3. The computer tomography apparatus ( 100) of claim 2, wherein λ_o<λs or λ_o>λR

4. The computer tomography apparatus ( 100) of claim 1 , wherein the reconstruction unit (118) is further adapted for differentiating the projection data on the basis of a Katsevich reconstruction scheme.

5. The computer tomography apparatus ( 100) of claim 1 , wherein a reconstruction of the first projected line results in first reconstruction data; wherein the reconstruction unit (118) is further adapted for: reconstructing a second projected line connecting the source path and the object point to be reconstructed, resulting in second reconstruction data; and performing a weighted average of the second reconstruction data and the first reconstruction data.

6. The computer tomography apparatus ( 100) of claim 1 , wherein the filtering is a Hubert filtering.

7. The computer tomography apparatus (100) of claim 1, further comprising: a collimator (105) arranged between the electromagnetic radiation source (104) and detecting elements (123); wherein the collimator (105) is adapted for collimating an electromagnetic radiation beam emitted by the electromagnetic radiation source (104) to form a cone-beam.

8. The computer tomography apparatus ( 100) of claim 1 , wherein the detecting elements (123) form a multi-slice detector array

(108).

9. The computer tomography apparatus (100) of claim 1 , configured as one of the group consisting of a baggage inspection apparatus, a medical application apparatus, a material testing apparatus and a material science analysis apparatus.

10. A method of examining an object of interest (107) with a computer tomography apparatus (100), the method comprising the steps of: differentiating projection data; filtering the projection data along a part of finite length of a first projected line, the line connecting the source path and an object point to be reconstructed, and wherein the part is limited by the projection of two points on the line, which are outside the object of interest (107); and back-projecting the filtered projection data over an interval comprising a PI interval of the object point.

11. An image processing device for examining an object of interest (107) with a computer tomography apparatus, the image processing device comprising: a memory for storing projection data; a reconstruction unit (118), being adapted for: differentiating proj ection data; filtering the projection data along a part of finite length of a first projected line, the line connecting the source path and an object point to be reconstructed, and wherein the part is limited by the projection of two points on the line, which are outside the object of interest (107); and back-projecting the filtered projection data over an interval comprising a

PI interval of the object point.

12. A computer-readable medium (402), in which a computer program of examining an object of interest (107) with a computer tomography apparatus (100) is stored which, when being executed by a processor (401), is adapted to carry out the steps of: differentiating projection data; filtering the projection data along a part of finite length of a first projected line, the line connecting the source path and an object point to be reconstructed, and wherein the part is limited by the projection of two points on the line, which are outside the object of interest (107); and back-projecting the filtered projection data over an interval comprising a PI interval of the object point.

13. A program element of examining an object of interest (107), which, when being executed by a processor (401), is adapted to carry out the steps of differentiating projection data; filtering the projection data along a part of finite length of a first projected line, the line connecting the source path and an object point to be reconstructed, and wherein the part is limited by the projection of two points on the line, which are outside the object of interest (107); and back-projecting the filtered projection data over an interval comprising a PI interval of the object point.