Method for reconstructing a three-dimensional image of an object scanned in the context of a tomosynthesis, and apparatus for tomosynthesis
First Claim
Patent Images
1. A tomosynthesis method for reconstructing a three-dimensional image of an object, comprising the steps of:
- providing an x-ray source having an x-ray focus;
providing a radiation detector;
disposing a three-dimensional object in a three-dimensional object space between said x-ray focus and said radiation detector;
scanning said object by moving at least said x-ray focus relative to said object to irradiate said object with x-rays from a plurality of different projection angles φ
;
detecting said x-rays attenuated by said object with said radiation detector at each of said projection angles φ
as respective projection images in a 2D recording geometry, each of said projection images comprising a set of projection image data of said object in a 2D projection image space;
applying a 2D filtering function H2Dfilter,φ
(ω
u,ω
v) to said sets of projection image data to obtain filtered sets of projection image data;
in a computer, individually back-projecting said filtered sets of projection image data into a 3D reconstruction image volume for producing a reconstruction image of said object; and
determining said 2D filtering function by the steps of;
calculating a 3D transmission function Hproj(ω
x,ω
y,ω
z) from the recording geometry for the individual sets of projection image data and back-projecting the individual sets of projection image data into the 3D reconstruction image volume;
inverting by approximation, the 3D transmission function Hproj(ω
x,ω
y,ω
z) and thereby determining an inversion function Hinv(ω
x,ω
y,ω
z);
producing a 3D filtering function Hopt(ω
x,ω
y,ω
z) dependent on at least one selected image characteristic of the reconstruction image;
determining a resulting 3D filtering function Hfilter(ω
x,ω
y,ω
z) by multiplying the 3D filtering function Hopt(ω
x,ω
y,ω
z) and the inversion function Hinv(ω
x,ω
y,ω
z); and
determining said 2D filtering function H2Dfilter,φ
(ω
u,ω
v) from the resulting 3D filtering function Hfilter(ω
x,ω
y,ω
z) by coordinate transformation of the 3D object space into the 2D projection image space of the respective individual sets of projection image data at the projection angles φ
.
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Abstract
In a method for reconstruction of a three-dimensional image of an object scanned in linear or circular fashion in the context of a tomosynthesis. The object is transirradiated with X-rays from various projection angles φ for the recording of the projection images, and the radiation exiting from the object is recorded by a detector that supplies digital output image signals. The output image signals representing the projection image data are supplied to a computer for image reconstruction. In the context of the reconstruction a filter is first produced, on the basis of the following steps: A 3D transmission function Hproj(ωx,ωy,ωz) is calculated from the recording geometry for the individual projection image recording and the back-projection of the individual projection images into the 3D reconstruction image volume. By approximation, the 3D transmission function Hproj(ωx,ωy,ωz) is inverted for the determination of an inversion function Hinv(ωx,ωy,ωz). A 3D filtering function Hopt(ωx,ωy,ωz) is produced dependent on one or more desired image characteristics of the reconstruction image. A resulting 3D filtering function Hfilter(ωx,ωy,ωz) is determined by multiplication of the 3D filtering function Hopt(ωx,ωy,ωz) and the inversion function Hinv(ωx,ωy,ωz). A 2D filtering function H2Dfilter,φ(ωu,ωv) is determined from the resulting 3D filtering function Hfilter(ωu,ωv ωz) by coordinate transformation of the 3D object space into the 2D projection image space of the respective individual projection images at the projection angle φ. After calculating the filter, the reconstruction of the image takes place in the computer by application of the 2D filtering function H2Dfilter,φ(ωu,ωv) to the associated individual projection image data, and production of the reconstruction image by back-projection of the filtered individual projection image data, into the 3D reconstruction image volume.
159 Citations
50 Claims
-
1. A tomosynthesis method for reconstructing a three-dimensional image of an object, comprising the steps of:
-
providing an x-ray source having an x-ray focus;
providing a radiation detector;
disposing a three-dimensional object in a three-dimensional object space between said x-ray focus and said radiation detector;
scanning said object by moving at least said x-ray focus relative to said object to irradiate said object with x-rays from a plurality of different projection angles φ
;
detecting said x-rays attenuated by said object with said radiation detector at each of said projection angles φ
as respective projection images in a 2D recording geometry, each of said projection images comprising a set of projection image data of said object in a 2D projection image space;
applying a 2D filtering function H2Dfilter,φ
(ω
u,ω
v) to said sets of projection image data to obtain filtered sets of projection image data;
in a computer, individually back-projecting said filtered sets of projection image data into a 3D reconstruction image volume for producing a reconstruction image of said object; and
determining said 2D filtering function by the steps of;
calculating a 3D transmission function Hproj(ω
x,ω
y,ω
z) from the recording geometry for the individual sets of projection image data and back-projecting the individual sets of projection image data into the 3D reconstruction image volume;
inverting by approximation, the 3D transmission function Hproj(ω
x,ω
y,ω
z) and thereby determining an inversion function Hinv(ω
x,ω
y,ω
z);
producing a 3D filtering function Hopt(ω
x,ω
y,ω
z) dependent on at least one selected image characteristic of the reconstruction image;
determining a resulting 3D filtering function Hfilter(ω
x,ω
y,ω
z) by multiplying the 3D filtering function Hopt(ω
x,ω
y,ω
z) and the inversion function Hinv(ω
x,ω
y,ω
z); and
determining said 2D filtering function H2Dfilter,φ
(ω
u,ω
v) from the resulting 3D filtering function Hfilter(ω
x,ω
y,ω
z) by coordinate transformation of the 3D object space into the 2D projection image space of the respective individual sets of projection image data at the projection angles φ
.- View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23)
approximating said 3D filtering function Hproj(ω
x,ω
y,ω
z) as a resulting 3D filtering function Hfilter(ω
x,ω
y,ω
z), independent of ω
z; and
using said resulting 3D filtering function Hfilter(ω
x,ω
y) as said 2D filtering function for filtering said projection image data sets to obtain said filtered sets of projection image data.
-
-
4. A method as claimed in claim 3 comprising the additional steps of:
-
identifying at least one selected tomogram in said 3D reconstruction volume; and
applying said resulting 3D filtering function Hfilter(ω
x,ω
y) as said 2D filtering function only to filter said projection image data sets for said at least one selected tomogram.
-
-
5. A method as claimed in claim 4 comprising the additional steps of:
-
providing a display monitor; and
immediately displaying said at least one selected tomogram on said display monitor after producing said reconstruction image thereof.
-
-
6. A method as claimed in claim 1 wherein the step of scanning said object comprises scanning said object by moving at least said x-ray focus relative to said object in a circular scanning path.
-
7. A method as claimed in claim 1 comprising the step of forming, by using said resulting 3D filtering function Hfilter(ω
-
x,ω
y,ω
z), a substantially homogenous slice profile of said reconstruction image, at least in a sub-region of said object space.
-
x,ω
-
8. A method as claimed in claim 1 wherein said object space includes an incompletely scanned region, and wherein said method comprises the additional steps of:
-
forming a spectral function Hspectrum(ω
x,ω
y) as a filter component of said resulting 3D filtering function Hfilter(ω
x,ω
y,ω
z); and
using said spectral function to eliminate all contributions to said reconstruction image arising from said incompletely scanned region.
-
-
9. A method as claimed in claim 1 wherein said object space includes an incompletely scanned region, and wherein said method comprises the additional steps of:
-
forming a spectral function Hspectrum(ω
x,ω
y) as a filter component of said resulting 3D filtering function Hfilter(ω
x,ω
y,ω
z); and
using said spectral function to give contributions from said incompletely scanned region a lower weight in said reconstruction image than contributions from other regions of said object space.
-
-
10. A method as claimed in claim 1 wherein said object space includes an incompletely scanned region which produces contributions having an inherent damping to said reconstruction image, said method comprising the additional steps of:
-
forming a spectral function Hspectrum(ω
x,ω
y) as a filter component of said resulting 3D filtering function Hfilter(ω
x,ω
y,ω
z); and
artificially equally weighting all contributions to said reconstruction image, including said contributions arising from said incompletely scanned region, for compensating for said inherent damping.
-
-
11. A method as claimed in claim 1 wherein said object space includes a scanned region which is scanned in the step of scanning said object, and wherein said scanned region has a scan edge, said scan edge producing a discontinuity in said reconstruction image, said method comprising the additional steps of:
-
forming a profile function Hprofile(ω
z) as one component of said resulting 3D filtering function Hfilter(ω
x,ω
y,ω
z); and
at least partially removing said discontinuities in said reconstruction image arising from said scan edge using said profile function Hprofile(ω
z).
-
-
12. A method as claimed in claim 11 wherein the step of at least partially removing said discontinuities comprises multiplying said profile function Hprofile(ω
- z) with a window function having a value equal to one everywhere within said scanned region, except said edge region, and falls continuously to zero at boundaries which are still within said scanned region.
-
13. A method as claimed in claim 11 wherein the step of at least partially removing said discontinuities comprises conducting a convolution of said profile function Hprofile(ω
- z) with a smoothing convolution core.
-
14. A method as claimed in claim 11 wherein the step of at least partially removing said discontinuities comprises conducting a locus-frequency-dependent scaling of ω
- z in said incompletely scanned region.
-
15. A method as claimed in claim 11 wherein the step of at least partially removing said discontinuities comprises a combination of scaling and smoothing contributions to said reconstruction image from said edge region using said profile function Hprofile(ω
- z).
-
16. A method as claimed in claim 1 comprising forming a profile function Hprofile(ω
-
φ
), as said 3D filtering function, that is weighted dependent on said projection angle.
-
φ
-
17. A mhethod as claimed in claim 16 comprising an increased contrast in said 3D reconstruction volume by using two identical sets of said projection images, processing said sets in different ways and afterwards mixing said sets, and filtering a first of said sets with an inverse 3D transfer function Hinv(ω
-
x, ω
y, ω
z) weighted by the profile function Hprofile(ω
φ
), and weighting a second of said sets by a function (1−
Hprofile(ω
φ
)).
-
x, ω
-
18. A method as claimed in claim 17 wherein said object space includes two identically dimensioned reconstruction volumes, and wherein the step of producing a reconstruction image of said object comprises producing respective reconstruction images of said two reconstruction volumes, with individual ones of said projection images contributing to a first of said two reconstruction volumes with a weighting Hprofile(ω
-
φ
) and which have been filtered with said inverse 3D transmission function Hinv(ω
x,ω
y,ω
z), and wherein individual ones of said projection images are employed without filtering thereof to contribute to a second of said two reconstruction volumes with a weighting of 1−
Hprofile(ω
φ
)), followed by mixing said two reconstruction volumes by superimposition with a mixing coefficient η
.
-
φ
-
19. A method as claimed in claim 18 wherein said two reconstruction volumes include at least one selected tomogram of said object selectable by selecting said mixing coefficient η
- , and wherein the step of mixing said two reconstruction volumes comprises mixing said two reconstruction volumes with a coefficient η
selected dependent on said selected tomogram.
- , and wherein the step of mixing said two reconstruction volumes comprises mixing said two reconstruction volumes with a coefficient η
-
20. A method as claimed in claim 19 comprising the additional step of immediately displaying said selected tomogram on a monitor.
-
21. A method as claimed in claim 1 wherein said reconstruction image includes a selected tomogram, and comprising the additional step of filtering said selected tomogram with a spectral function Hspectrum(ω
-
x,ω
y) having a type an parameterization which are variable.
-
x,ω
-
22. A method as claimed in claim 21 comprising the step of immediately displaying said selected tomogram on a monitor together with an identification of at least one of said type and said parameterization associated with said selected tomogram.
-
23. A method as claimed in claim 1 comprising the step of using said result 3D filtering function Hfilter(ω
-
x, ω
y, ω
z), of if necessary, a further 3D filtering function, where a spatial-frequency-dependent scaling in the ω
z argument is conducted over the entire frequency region measured in the step of scanning said object.
-
x, ω
-
24. A tomosynthesis method for reconstructing a three-dimensional image of an object, comprising the steps of:
-
providing an x-ray source having an x-ray focus;
providing a radiation detector;
disposing a three-dimensional object in a three-dimensional object space between said x-ray focus and said radiation detector;
scanning said object by moving at least said x-ray focus relative to said object to irradiate said object with x-rays from a plurality of different projection angles φ
;
detecting said x-rays attenuated by said object with said radiation detector at each of said projection angles φ
as respective projection images in a 2D recording geometry, each of said projection images comprising a set of projection image data of said object in a 2D projection image space;
in a computer, individually back-projecting the said sets of projection image data into a 3D reconstruction image volume for producing a reconstruction image of said object;
applying a 3D filtering function Hfilter(ω
x,ω
y,ω
z) to said reconstruction image of said object to obtain a filtered reconstruction image; and
determining said 3D filtering function by the steps of;
calculating a 3D transmission function Hproj(ω
x,ω
y,ω
z) from the recording geometry for the individual sets of projection image data and back-projecting the individual sets of projection image data into the 3D reconstruction image volume;
inverting by approximation, the 3D transmission function Hproj(ω
x,ω
y,ω
z) and thereby determining an inversion function Hinv(ω
x,ω
y,ω
z);
producing a 3D filtering function Hopt(ω
x,ω
y,ω
z) dependent on at least one selected image characteristic of the reconstruction image;
determining a resulting 3D filtering function Hfilter(ω
x,ω
y,ω
z) by multiplying the 3D filtering function Hopt(ω
x,ω
y,ω
z) and the inversion function Hinv(ω
x,ω
y,ω
z).- View Dependent Claims (25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46)
approximating said 3D filtering function Hproj(ω
x,ω
y,ω
z) as a resulting 3D filtering A function Hfilter(ω
x,ω
y,ω
z), independent of ω
z; and
using said resulting 3D filtering function Hfilter(ω
x,ω
y) as said 2D filtering function for filtering said tomograms.
-
-
27. A method as claimed in claim 26 comprising the additional steps of:
identifying at least one selected tomogram in said 3D reconstruction volume; and
applying said resulting 3D filtering function Hfilter(ω
x,ω
y) only to filter said at least one selected tomogram.
-
28. A method as claimed in claim 27 comprising the additional steps of:
-
providing a display monitor; and
immediately displaying said at least one selected tomogram on said display monitor after producing said reconstruction image thereof.
-
-
29. A method as claimed in claim 24 wherein the step of scanning said object comprises scanning said object by moving at least said x-ray focus relative to said object in a circular scanning path.
-
30. A method as claimed in claim 24 comprising the step of forming, by using said resulting 3D filtering function Hfilter(ω
-
x,ω
y,ω
z), a substantially homogenous slice profile of said reconstruction image, at least in a sub-region of said object space.
-
x,ω
-
31. A method as claimed in claim 24 wherein said object space includes an incompletely scanned region, and wherein said method comprises the additional steps of:
-
forming a spectral function Hspectrum(ω
x,ω
y) as a filter component of said resulting 3D filtering function Hfilter(ω
x,ω
y,ω
z); and
using said spectral function to eliminate all contributions to said reconstruction image arising from said incompletely scanned region.
-
-
32. A method as claimed in claim 24 wherein said object space includes an incompletely scanned region, and wherein said method comprises the additional steps of:
-
forming a spectral function Hspectrum(ω
x,ω
y) as a filter component of said resulting 3D filtering function Hfilter(ω
x,ω
y,ω
z); and
using said spectral function to give contributions from said incompletely scanned region a lower weight in said reconstruction image than contributions from other regions of said object space.
-
-
33. A method as claimed in claim 24 wherein said object space includes an incompletely scanned region which produces contributions having an inherent damping to said reconstruction image, said method comprising the additional steps of:
-
forming a spectral function Hspectrum(ω
x,ω
y) as a filter component of said resulting 3D filtering function Hfilter(ω
x,ω
y,ω
z); and
artificially equally weighting all contributions to said reconstruction image, including said contributions arising from said incompletely scanned region, for compensating for said inherent damping.
-
-
34. A method as claimed in claim 24 wherein said object space includes a scanned region which is scanned in the step of scanning said object, and wherein said scanned region has a scan edge, said scan edge producing a discontinuity in said reconstruction image, said method comprising the additional steps of:
-
forming a profile function Hprofile(ω
z) as one component of said resulting 3D filtering function Hfilter(ω
x,ω
y,ω
z); and
at least partially removing said discontinuities in said reconstruction image arising from said scan edge using said profile function Hprofile(ω
z).
-
-
35. A method as claimed in claim 34 wherein the step of at least partially removing said discontinuities comprises multiplying said profile function Hprofile(ω
- z) with a window function having a value equal to one everywhere within said scanned region, except said edge region, and falls continuously to zero at boundaries which are still within said scanned region.
-
36. A method as claimed in claim 34 wherein the step of at least partially removing said discontinuities comprises conducting a convolution of said profile function Hprofile(ω
- z) with a smoothing convolution core.
-
37. A method as claimed in claim 34 wherein the step of at least partially removing said discontinuities comprises conducting a locus-frequency-dependent scaling of ω
- z in said incompletely scanned region.
-
38. A method as claimed in claim 34 wherein the step of at least partially removing said discontinuities comprises a combination of scaling and smoothing contributions to said reconstruction image from said edge region using said profile function Hprofile(ω
- z).
-
39. A method as claimed in claim 24 comprising forming a profile function Hprofile(ω
-
φ
) as said 3D filtering function, that is weighted dependent on said projection angle.
-
φ
-
40. A method as claimed in claim 39 comprising an increased contrast in said 3D reconstruction volume by filtering said 3D reconstruction volume with a filter consisting of
-
41. A method as claimed in claim 37 wherein said object space includes two identically dimensioned reconstruction volumes, and wherein the step of producing a reconstruction image of said object comprises producing respective reconstruction images of said two reconstruction volumes, with individual ones of said projection images contributing to a first of said two reconstruction volumes filtered by Hprofile(ω
-
φ
) and with said inverse 3D transmission function Hinv(ω
x,ω
y,ω
z), and to a second of said two reconstruction volumes filtered by (1−
Hprofile(ω
φ
)), followed by mixing said two reconstruction volumes by superimposition with a mixing coefficient η
.
-
φ
-
42. A method as claimed in claim 41 wherein said two reconstruction volumes include at least one selected tomogram of said object selectable by selecting said mixing coefficient η
- and wherein the step of mixing said two reconstruction volumes comprises mixing said two reconstruction volumes with a coefficient η
selected dependent on said selected tomogram.
- and wherein the step of mixing said two reconstruction volumes comprises mixing said two reconstruction volumes with a coefficient η
-
43. A method as claimed in claim 42 comprising the additional step of immediately displaying said selected tomogram on a monitor.
-
44. A method as claimed in claim 24 wherein said reconstruction image includes a selected tomogram, and comprising the additional step of filtering said selected tomogram with a spectral function Hspetrum(ω
-
x,ω
y) having a type an parameterization which are variable.
-
x,ω
-
45. A method as claimed in claim 44 comprising the step of immediately displaying said selected tomogram on a monitor together with an identification of at least one of said type and said parameterization associated with said selected tomogram.
-
46. A method as claimed in claim 24 comprising the step of using said resulting 3D filtering function Hfilter(ω
-
x, ω
y, ω
z), or if necessary, a further 3D filtering function, where a spatial-frequency-dependent scaling in the ω
z argument is conducted over the entire frequency region measured in the step of scanning said object.
-
x, ω
-
47. A tomosynthesis apparatus for reconstructing a three-dimensional irmiage of an object, comprising:
-
an x-ray source having an x-ray focus;
a radiation detector disposed to detect x-rays attenuated by a three-dimensional object in a three-dimensional object space between said x-ray focus and said radiation detector;
means for moving at least said x-ray focus relative to said object to scan said object by irradiating said object with x-rays from a plurality of different projection angles φ
;
said radiation detector detecting said x-rays attenuated by said object with at each of said projection angles φ
as respective projection images in a 2D recording geometry, each of said projection images comprising a set of projection image data of said object in a 2D projection image space;
means for applying a 2D filtering function H2Dfilter,φ
(ω
u,ω
v) to said sets of projection image data to obtain filtered sets of projection image data;
computer means for individually back-projecting said filtered sets of projection image data into a 3D reconstruction image volume for producing a reconstruction image of said object; and
said means for applying said 2D filtering function comprising means for determining said 2D filtering function by calculating a 3D transmission function Hproj(ω
x,ω
y,ω
z) from the recording geometry for the individual sets of projection image data and back-projecting the individual sets of projection image data into the 3D reconstruction image volume, thereby determining an inversion function Hinv(ω
x,ω
y,ω
z), producing a 3D filtering function Hopt(ω
x,ω
y,ω
z) dependent on at least one selected image characteristic of the reconstruction image, determining a resulting 3D filtering function Hfilter(ω
x,ω
y,ω
z) by multiplying the 3D filtering function Hopt(ω
x,ω
y,ω
z) and the inversion function Hinv(ω
x,ω
y,ω
z), and determining said 2D filtering function H2Dfilter,φ
(ω
u,ω
v) frorn the resulting 3D filtering function Hfilter(ω
x,ω
y,ω
z) by coordinate transformation of the 3D object space into the 2D projection image space of the respective individual sets of projection image data at the projection angles φ
.- View Dependent Claims (48)
-
-
49. A tomosynthesis apparatus for reconstructing a three-dimensional image of an object, comprising:
-
an x-ray source having an x-ray focus;
a radiation detector disposed to detect x-rays attenuated by a three-dimensional object in a three-dimensional object space between said x-ray focus and said radiation detector;
means for moving at least said x-ray focus relative to said object to scan said object by irradiating said object with x-rays from a plurality of different projection angles said radiation detector detecting said x-rays attenuated by said object with at each of said projection angles φ
as respective projection images in a 2D recording geometry, each of said projection images comprising a set of projection image data of said object in a 2D projection image space;
computer means for individually back-projecting said sets of projection image data into a 3D reconstruction image volume for producing a reconstruction image of said object;
means for applying a 3D filtering function Hfilter(ω
x,ω
y,ω
z) to said reconstruction image of said object to obtain a filtered reconstruction object; and
said means for applying said 3D filtering function comprising means for determining said 3D filtering function by calculating a 3D transmission function Hproj(ω
x,ω
y,ω
z) from the recording geometry for the individual sets of projection image data and back-projecting the individual sets of projection image data into the 3D reconstruction image volume, inverting by approximation, the 3D transmission function Hproj(ω
x,ω
y,ω
z) and thereby determining an inversion function Hinv(ω
x,ω
y,ω
z), producing a 3D filtering function Hopt(ω
x,ω
y,ω
z) dependent on at least one selected image characteristic of the reconstruction image, and determining a resulting 3D filtering function Hfilter(ω
x,ω
y,ω
z) by multiplying the 3D filtering function Hopt(ω
x,ω
y,ω
z) and the inversion function Hinv(ω
x,ω
y,ω
z) and determining a resulting 3D filtering function Hfilter,φ
(ω
x,ω
y,ω
z by multiplying the 3D filtering function Hfilter((ω
x,ω
y,ω
z), and the inversion function Hinv(ω
x,ω
y,ω
z).- View Dependent Claims (50)
-
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-
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Current AssigneeSiemens Healthcare GMBH (Siemens AG)
-
Original AssigneeSiemens AG
-
InventorsZellerhoff, Michael, Lauritsch, Guenter, Haerer, Wolfgang
-
Primary Examiner(s)Boudreau, Leo
-
Assistant Examiner(s)CHOOBIN, BARRY
-
Application NumberUS09/207,125Time in Patent Office1,359 DaysField of Search382/128, 382/100, 128/922, 250/455.11, 600/409US Class Current382/128CPC Class CodesG01N 2223/419 computed tomographG01N 23/044 using laminography or tomos...G01N 23/046 using tomography, e.g. comp...G06T 11/006 Inverse problem, transforma...G06T 2211/421 Filtered back projection [FBP]G06T 2211/436 Limited angle
