WO2005107598A1 - Efficient circle and line cone beam computed tomography - Google Patents
Efficient circle and line cone beam computed tomography Download PDFInfo
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- WO2005107598A1 WO2005107598A1 PCT/US2004/012536 US2004012536W WO2005107598A1 WO 2005107598 A1 WO2005107598 A1 WO 2005107598A1 US 2004012536 W US2004012536 W US 2004012536W WO 2005107598 A1 WO2005107598 A1 WO 2005107598A1
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- 238000007408 cone-beam computed tomography Methods 0.000 title description 2
- 238000000034 method Methods 0.000 claims abstract description 73
- 238000001914 filtration Methods 0.000 claims description 46
- 239000013598 vector Substances 0.000 claims description 11
- 238000013527 convolutional neural network Methods 0.000 claims description 9
- 230000006870 function Effects 0.000 claims description 3
- 238000007781 pre-processing Methods 0.000 claims 4
- 239000002243 precursor Substances 0.000 claims 2
- 230000008901 benefit Effects 0.000 description 5
- 238000002591 computed tomography Methods 0.000 description 5
- 238000002360 preparation method Methods 0.000 description 4
- 230000009286 beneficial effect Effects 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 230000003362 replicative effect Effects 0.000 description 2
- 238000010276 construction Methods 0.000 description 1
- 238000013480 data collection Methods 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 238000002059 diagnostic imaging Methods 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 238000003384 imaging method Methods 0.000 description 1
- 230000033001 locomotion Effects 0.000 description 1
- 239000011159 matrix material Substances 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 230000010076 replication Effects 0.000 description 1
Classifications
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B6/00—Apparatus or devices for radiation diagnosis; Apparatus or devices for radiation diagnosis combined with radiation therapy equipment
- A61B6/02—Arrangements for diagnosis sequentially in different planes; Stereoscopic radiation diagnosis
- A61B6/03—Computed tomography [CT]
- A61B6/032—Transmission computed tomography [CT]
-
- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B6/00—Apparatus or devices for radiation diagnosis; Apparatus or devices for radiation diagnosis combined with radiation therapy equipment
- A61B6/02—Arrangements for diagnosis sequentially in different planes; Stereoscopic radiation diagnosis
- A61B6/027—Arrangements for diagnosis sequentially in different planes; Stereoscopic radiation diagnosis characterised by the use of a particular data acquisition trajectory, e.g. helical or spiral
Definitions
- This invention is a Continuation-In-Part of United States Patent Application Serial No. 10/728, 136, filed December 4, 2003 which claims the benefit of priority to U.S. Provisional Application, Serial No. 60/430,802 filed, December 4, 2002, and is a Continuation-In-Part of United States Patent Application Serial No. 10/389,534 filed March 14, 2003 which is a Continuation-In-Part of Serial No. 10/389,090 filed March 14, 2003, which is a Continuation-In-Part of Serial No. 10/143,160 filed May 10, 2002 now U.S. Patent 6,574,299, which claims the benefit of priority to U.S. Provisional Application 60/312,827 filed August 16, 2001.
- This invention relates to computer tomography, and in particular to processes, methods and systems for reconstructing three dimensional images from the data obtained by a circle and line scan of an object, such as when the object first moves through a C- arm, and then the C-arm rotates around either a non moving or a moving object.
- CT computer tomography
- spiral type scanning has become the preferred process for data collection in CT.
- a table with the patient continuously moves at a constant speed through the gantry that is continuously rotating about the table.
- spiral scanning has used one-dimensional detectors, which receive data in one dimension (a single row of detectors).
- two-dimensional detectors where multiple rows (two or more rows) of detectors sit next to one another, have been introduced.
- CT there have been significant problems for image reconstruction especially for two-dimensional detectors.
- Data provided by the two- dimensional detectors will be referred to as cone-beam (CB) data or CB projections.
- CB cone-beam
- non-spiral scans in which the trajectory of the x-ray source is different from spiral.
- Fig. 1 shows a typical prior art arrangement of a patient on a table that moves through a C-arm device, that is capable of rotating around the patient, having an x-ray tube source and a detector array, where cone beam projection data sets are received by the x-ray detector, and an image reconstruction process takes place in a computer with a display for the reconstructed image.
- C-arm devices to reconstruct data.
- a primary objective of the invention is to provide improved processes, methods and systems for reconstructing images of objects that have been scanned with two- dimensional detectors.
- a secondary objective of the invention is to provide improved processes, methods and systems for reconstructing images of objects scanned with a circle and line x-ray source trajectory that is able to reconstruct an exact image and not an approximate image.
- a third objective of the invention is to provide improved processes, methods and systems for reconstructing images of objects scanned with a circle and line x-ray source trajectory that creates an exact image in an efficient manner using a filtered back projection (FBP) structure.
- FBP filtered back projection
- a fourth objective of the invention is to provide improved processes, methods and systems for reconstructing images of objects scanned with a circle and line x-ray source trajectory that creates an exact image with minimal computer power.
- a fifth objective of the invention is to provide improved processes, methods and systems for reconstructing images of objects scanned with a circle and line x-ray source trajectory that creates an exact image utilizing a convolution-based FBP structure.
- a sixth objective of the invention is to provide improved processes, methods and systems for reconstructing images of objects scanned with a circle and line x-ray source trajectory that is CB projection driven allowing for the algorithm to work simultaneously with the CB data acquisition.
- a seventh objective of the invention is to provide improved processes, methods and systems for reconstructing images of objects scanned with a circle and line x-ray source trajectory that does not require storing numerous CB projections in computer memory.
- An eighth objective of the invention is to provide improved processes, methods and systems for reconstructing images of objects scanned with a circle and line x-ray source trajectory that allows for almost real time imaging to occur where images are displayed as soon as a slice measurement is completed.
- a preferred embodiment of the invention uses a seven overall step process for reconstructing the image of an object under a circle and line scan. In a first step a current CB projection is measured. Next, a family of lines is identified on a detector according to a novel algorithm.
- the circle and line scanning can include a partial planar curve scan before or after a line scan.
- the planar curved scan can be less than a full circle and even greater than a full circle. Additional and subsequent circle and line scans can be done consecutively after a first circle and line scan.
- Fig. 1 shows a typical prior art view arrangement of a patient on a table that moves through a C-arm device, that is capable of rotating around the patient, having an x-ray tube source and a detector array, where cone beam projection data sets are received by the x-ray detector, and an image reconstruction process takes place in a computer with a display for the reconstructed image.
- Fig. 2 shows an overview of the basic process steps of the invention.
- Fig. 3 shows mathematical notations of the circle and line scan.
- Fig. 4 illustrates a stereographic projection from the current source position on to the detector plane used in the algorithm for the invention.
- Fig. 5 illustrates finding of a filtering line for a reconstruction point x when the x-ray source is on the line.
- Fig. 6 illustrates finding of a filtering line for a reconstruction point x when the x-ray source is on the circle.
- Fig. 7 illustrates a family of lines used in the algorithm of the invention corresponding to the case when the x-ray source is on the line.
- Fig. 8 illustrates a family of lines used in the algorithm of the invention corresponding to the case when the x-ray source is on the circle.
- Fig. 9 is a three substep flow chart for identifying the set of lines, which corresponds to step 20 of Fig. 2.
- Fig. 10 is a seven substep flow chart for preparation for filtering, which corresponds to step 40 of Fig. 2.
- Fig. 11 is a seven substep flow chart for filtering, which corresponds to step 50.of Fig. 2.
- Fig. 12 is an eight substep flow chart for backprojection, which corresponds to step 60 of Fig. 2.
- Fig. 1 shows a typical prior art view arrangement of a patient on a table that moves through a C-arm device such as the AXIOM Artis MP, manufactured by Siemens, that is capable of rotating around the patient, having an x-ray tube source and a detector array, where CB projections are received by the x-ray detector, and an image reconstruction process takes place in a computer 4 with a display 6 for displaying the reconstructed image.
- the detector array is a two- dimensional detector array.
- the array can include two, three or more rows of plural detectors in each row.
- FIG. 2 shows an overview of the basic process steps of the invention that occur during the image reconstruction process occurring in the computer 4 using a first embodiment. An overview of the invention process will now be described.
- a preferred embodiment works with keeping several (approximately 2 to approximately 4) CB projections in computer memory at a time and uses one family of lines.
- a current CB(cone beam) projection set is taken.
- the next steps 20 and 30 identify sets of lines on a virtual x-ray detector array according to the novel algorithm, which will be explained later in greater detail. In the given description of the algorithm the detector array can be considered to be flat, so the selected line can be a straight tilted line across the array.
- the next step 40 is the preparation for the filtering step, which includes computations of the necessary derivative of the CB projection data for the selected lines.
- the next step 50 is the convolution of the computed derivative (the processed CB data) with a filter along lines from the selected family of lines. This step can also be described as shift-invariant filtering of the derivative of the CB projection data.
- TL(x) intersects C at two points. One of them is y 0 , and the second is denoted
- the first one I x (x) c I x corresponds to the section of L between y 0 and y L (x) .
- the second one I 2 (x) a I 2 corresponds to the section of C between y 0 and
- S 2 is the unit sphere
- / is the function representing the distribution of the x-ray attenuation coefficient inside the object being scanned
- ⁇ is a unit vector
- D f (y,®) is the cone beam transform of /
- ⁇ (s,x) is the unit vector from the focal point y(s) pointing towards the reconstruction point x .
- h be the height of y(s) above the plane of the circle.
- DP(s) contains the z -axis and perpendicular to the shortest line segment connecting
- the origin is at (0, 0, h)
- the first axis is horizontal
- the second axis is vertical.
- the projected circle C is a parabola, which opens downward.
- j>(5) is the velocity vector of the source at the current position.
- Step 50 which is shift-invariant
- ⁇ denotes polar angle within a
- Equation (12) is of convolution type and one application of Fast Fourier
- FFT Fast Fourier Transform
- Equations (10) and (12) would represent that the resulting algorithm is of the convolution-based FBP type.
- processing of every CB projection consists of two steps. First, shift-invariant and x -independent filtering along a family of lines on the detector is performed. Second, the result is back-projected to update the image matrix.
- a property of the back-projection step is that for any point x on the detector the value obtained by filtering at x is used for all points x on the line segment connecting the current source position y(s) with x . Since d/dq in (12) is a local operation, each CB
- Step 10 We load the current CB(cone beam) projection into computer memory.
- the detector plane corresponding to the x-ray source located at y(s 0 ) is denoted DP(s Q ) .
- Fig. 9 is a three substep flow chart for identifying the set of lines, which
- Step 21 Choose a discrete set of values of the parameter s t inside the interval
- Step 22 For each s, chosen in Step 21 find a line tangent to the projected circle c. Step 23.
- the collection of lines constructed in Step 22 is the required set of lines (see Fig. 7 which illustrates the family of lines used in the algorithm of the invention).
- Step 30 Here we assume that the x-ray source is located on the circle C .
- Fig. 8 we form a set of lines parallel to the projection of the circle that cover the projection of the region of interest (ROI) inside the object being scanned.
- ROI region of interest
- Step 40 Preparation for filtering Fig. 10 is a seven substep flow chart for preparation for filtering, which corresponds to step 40 of Fig. 2, which will now be described.
- Step 41 If the x-ray source is located on the line L, fix a filtering line L ⁇ t e —] from the set of lines obtained in Step 20. If the x-ray source is located on the circle C , fix a filtering line L flt e_ 2 from the set of lines obtained in Step 30.
- Step 42 Parameterize points on the said line by polar angle ⁇ in the plane through y(s 0 ) and L ⁇ t .
- Step 43 Choose a discrete set of equidistant values ⁇ ⁇ that will be used later for discrete filtering in Step 50.
- Step 44 For each ⁇ ] find the unit vector ⁇ ⁇ which points from y(s 0 ) towards the point on L ⁇ t that corresponds to ⁇ .
- Step 45 Using the CB projection data D f (y(q),&) for a few values of q close to s 0 find numerically the derivative (d/dq)D j (y(q),&)
- for all ⁇ ⁇ ⁇ .
- Step 46 Store the computed values of the derivative in computer memory.
- Step 47 Repeat Steps 41-46 for all lines L ⁇ t . This way we will create the processed CB data ⁇ (_? 0 , ? ) corresponding to the x-ray source located at y(s 0 ) .
- Fig. 11 is a seven substep flow chart for filtering, which corresponds to step 50 of Fig. 2, which will now be described.
- Step 51 Fix a filtering line L ⁇ t . If the x-ray source is located on the line L , we takeZ ⁇ e_ j . If the x-ray source is located on the circle , we takeZ ⁇ e_ 2 .
- Step 52 Compute FFT (Fast Fourier Transform) of the values of the said processed CB data computed in Step 40 along the said line.
- Step 53 Compute FFT of the filter 1 / sin ⁇
- Step 54 Multiply FFT of the filter 1/sin/ (the result of Steps 53) and FFT of the values of the said processed CB data (the result of Steps 52).
- Step 55 Take the inverse FFT of the result of Step 54.
- Step 56 Store the result of Step 55 in computer memory.
- Step 57 Repeat Steps 51 -56 for all lines in the said family of lines. This will give the filtered CB data ⁇ (s 0 , ⁇ j ) .
- the filtering step can be well known in the field and can be implemented, for example, as shown and described in U.S. Patent 5,881,123 to Tarn, which is incorporated by reference.
- Fig. 12 is an eight substep flow chart for backprojection, which corresponds to step 60 of Fig. 2, which will now be described.
- Step 61. Fix a reconstruction point x , which represents a point inside the patient where it is required to reconstruct the image.
- Step 62 If ⁇ o belongs to I ⁇ (x) I 2 (x) , then the said filtered CB data affects the image at x and one performs Steps 63-68. If s 0 is not inside I ⁇ (x) u I 2 (x) , then the said filtered CB data is not used for image reconstruction at x . In this case go back to Step 61 and choose another reconstruction point.
- Step 63 Find the projection x of x onto the detector plane DP(s 0 ) and the unit vector ⁇ (s 0 ,x) , which points from y(s 0 ) towards x .
- Step 65 With interpolation estimate the value of ⁇ (s 0 , ⁇ (s 0 ,x)) from the said values of ⁇ (s 0 , ⁇ j ) for ⁇ close to ⁇ (s Q ,x) .
- Step 66 Compute the contribution from the said filtered CB data to the image being reconstructed at the point x by multiplying ⁇ (s 0 , ⁇ (s 0 ,x)) by
- Step 67 Add the said contribution to the image being reconstructed at the point x according to a pre-selected scheme (for example, the Trapezoidal scheme) for approximate evaluation of the integral in equation (10).
- Step 68 Go to Step 61 and choose a different reconstruction point x .
- Step 70 Go to Step 10 (Fig. 2) and load the next CB projection into computer memory.
- the image can be displayed at all reconstruction points x for which the image reconstruction process has been completed (that is, all the subsequent CB projections are not needed for reconstructing the image at those points). Discard from the computer memory all the CB projections that are not needed for image reconstruction at points where the image reconstruction process has not completed.
- the algorithm concludes when the scan is finished or the image reconstruction process has completed at all the required points.
- the invention is not limited to an object that undergoes a scan consisting of a single circle and a single line segment.
- the algorithm can be applied to trajectories consisting of several circles and line segments by applying it to various circle and line pairs, and then combining the results.
- the algorithm can be applied to trajectories in which a planar curve is not necessarily a circle, but, for example, an ellipse, and the like.
- Embodiments of the invention are possible. For example, one can integrate by parts in equation (6) as described in the inventor's previous U.S. Patent Application Serial No. 10/143,160 filed May 10, 2002 now U.S. Patent 6,574,299, now incorporated by reference, to get an exact convolution-based FBP-type inversion formula which requires keeping only one CB projection in computer memory.
- the algorithmic implementation of this alternative embodiment can be similar to and include the algorithmic implementation of Embodiment Two in the inventor's previous U.S. Patent Application Serial No. 10/143,160 filed May 10, 2002 now U.S. Patent 6,574,299, now incorporated by reference. The corresponding equations will now be described.
- V ⁇ D denotes the derivative of D f with respect to the angular variables along the
- u 1 denotes the set of unit vectors perpendicular to u .
- I k (x) [s bk (x),s lk (x)] . Integrating by parts with respect to s in equation (6) and using
- ⁇ k (s,x) is a constant with respect to s within each I k (x) (so it can be replaced by
- the invention can be used with rotating gantry devices.
- the amount of rotating can include a single rotational curve of at least approximately 5 degrees up to approximately 360 degrees or greater. Theoretically, there is no limit on the minimum range of rotation. Under realistic practical circumstances, a minimum range of rotation is between approximately 10 and approximately 20 degrees.
- the circle and line scanning of an object can have a line scanning before or after a single rotational curve scan as defined above. Subsequent circle and line scanning can occur as needed for image reconstruction.
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Priority Applications (3)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US10/523,867 US7197105B2 (en) | 2001-08-16 | 2004-04-23 | Efficient image reconstruction algorithm for the circle and line cone beam computed tomography |
US11/037,968 US7305061B2 (en) | 2001-08-16 | 2005-01-18 | Efficient image reconstruction algorithm for the circle and arc cone beam computer tomography |
US11/239,605 US7280632B2 (en) | 2001-08-16 | 2005-09-29 | Exact filtered back projection (FBP) algorithm for spiral computer tomography with variable pitch |
Applications Claiming Priority (6)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US10/728,136 | 2003-12-04 | ||
PCT/US2003/038375 WO2004051431A2 (en) | 2002-12-04 | 2003-12-04 | 3pi algorithm for spiral ct |
USPCT/US03/38375 | 2003-12-04 | ||
US10/728,136 US7010079B2 (en) | 2001-08-16 | 2003-12-04 | 3PI algorithm for spiral CT |
PCT/US2003/041114 WO2004084137A2 (en) | 2003-03-14 | 2003-12-24 | Efficient variable pitch spiral computed tomography algorithm |
USPCT/US03/41114 | 2003-12-24 |
Related Parent Applications (3)
Application Number | Title | Priority Date | Filing Date |
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US10/389,534 Continuation-In-Part US6804321B2 (en) | 2001-08-16 | 2003-03-14 | Filtered back projection (FBP) algorithm for computer tomography |
US10/728,136 Continuation-In-Part US7010079B2 (en) | 2001-08-16 | 2003-12-04 | 3PI algorithm for spiral CT |
PCT/US2003/041114 Continuation-In-Part WO2004084137A2 (en) | 2001-08-16 | 2003-12-24 | Efficient variable pitch spiral computed tomography algorithm |
Related Child Applications (3)
Application Number | Title | Priority Date | Filing Date |
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US10523867 A-371-Of-International | 2004-04-23 | ||
US11/037,968 Continuation-In-Part US7305061B2 (en) | 2001-08-16 | 2005-01-18 | Efficient image reconstruction algorithm for the circle and arc cone beam computer tomography |
US11/239,605 Continuation-In-Part US7280632B2 (en) | 2001-08-16 | 2005-09-29 | Exact filtered back projection (FBP) algorithm for spiral computer tomography with variable pitch |
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Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN110974278A (en) * | 2019-12-21 | 2020-04-10 | 电子科技大学 | DSA (digital Signal amplification) cone beam precise filtering back-projection tomography system and imaging method |
CN115105108A (en) * | 2022-06-30 | 2022-09-27 | 赛诺威盛科技(北京)股份有限公司 | Defocus calibration method and device, defocus calibration mold body and electronic device |
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US5170439A (en) * | 1991-06-11 | 1992-12-08 | Picker International, Inc. | Cone beam reconstruction using combined circle and line orbits |
US6292525B1 (en) * | 1999-09-30 | 2001-09-18 | Siemens Corporate Research, Inc. | Use of Hilbert transforms to simplify image reconstruction in a spiral scan cone beam CT imaging system |
-
2004
- 2004-04-23 WO PCT/US2004/012536 patent/WO2005107598A1/en active Application Filing
Patent Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
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US5170439A (en) * | 1991-06-11 | 1992-12-08 | Picker International, Inc. | Cone beam reconstruction using combined circle and line orbits |
US6292525B1 (en) * | 1999-09-30 | 2001-09-18 | Siemens Corporate Research, Inc. | Use of Hilbert transforms to simplify image reconstruction in a spiral scan cone beam CT imaging system |
Cited By (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN110974278A (en) * | 2019-12-21 | 2020-04-10 | 电子科技大学 | DSA (digital Signal amplification) cone beam precise filtering back-projection tomography system and imaging method |
CN110974278B (en) * | 2019-12-21 | 2022-02-11 | 电子科技大学 | DSA (digital Signal amplification) cone beam precise filtering back-projection tomography system and imaging method |
CN115105108A (en) * | 2022-06-30 | 2022-09-27 | 赛诺威盛科技(北京)股份有限公司 | Defocus calibration method and device, defocus calibration mold body and electronic device |
CN115105108B (en) * | 2022-06-30 | 2023-06-09 | 赛诺威盛科技(北京)股份有限公司 | Defocus correction method and device, defocus correction die body and electronic device |
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