System and method for regularized reconstruction of phase contrast computerized tomography
Reconstructing under-sampled PCT data includes obtaining under-sampled scan data of a subject-under-test, the object scan performed on a phase contrast computed tomography (PCT) system, performing a regularized Fourier analysis on the under-sampled scan data, correcting for one or more PCT system contributions to the under-sampled scan data by dividing the computed Fourier coefficients by Fourier coefficients representative of the one or more PCT system contributions, obtaining at least one of an absorption sinogram, a differential phase sinogram, and a dark field sinogram from the corrected Fourier coefficients, and performing tomographic reconstruction on the obtained absorption sinogram, the obtained differential phase sinogram, and the obtained dark field sinogram. A system and non-transitory computer readable medium are also disclosed.
1. A method for reconstructing under-sampled phase contrast computed tomography data, the method comprising:
obtaining under-sampled scan data of a subject-under-test, the object scan performed on a phase contrast computed tomography (PCT) system;
performing a regularized Fourier analysis on the under-sampled scan data;
correcting for one or more PCT system contributions to the under-sampled scan data by dividing the computed Fourier coefficients by Fourier coefficients representative of the one or more PCT system contributions;
obtaining at least one of an absorption sinogram, a differential phase sinogram, and a dark field sinogram from the corrected Fourier coefficients; and
performing tomographic reconstruction on the obtained absorption sinogram, the obtained differential phase sinogram, and the obtained dark field sinogram.
2. The method of claim 1 , including collecting the under-sampled object scan data in a randomized manner.
3. The method of claim 1 , including obtaining the Fourier coefficients representative of the one or more PCT system contributions by performing an air scan.
4. The method of claim 1 , wherein the dividing step corrects the computed Fourier coefficients for PCT system non-homogeneities.
5. The method of claim 1 , the regularized Fourier analysis step including solving a minimization equation expressed as
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6. The method of claim 1 , wherein the regularized Fourier analysis step includes the correcting step.
7. The method of claim 6 , including the regularized Fourier analysis step including solving a minimization equation expressed as
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8. A non-transitory computer-readable medium having stored thereon instructions which when executed by a processor cause the processor to perform a method for reconstructing under-sampled phase contrast computed tomography data, the method comprising:
obtaining under-sampled scan data of a subject-under-test, the object scan performed on a phase contrast computed tomography (PCT) system;
performing a regularized Fourier analysis on the under-sampled scan data;
computing Fourier coefficients for the under-sampled scan data;
correcting for one or more PCT system contributions to the under-sampled scan data by dividing the computed Fourier coefficients by Fourier coefficients representative of the one or more PCT system contributions;
obtaining at least one of an absorption sinogram, a differential phase sinogram, and a dark field sinogram from the corrected Fourier coefficients; and
performing tomographic reconstruction on the obtained absorption sinogram, the obtained differential phase sinogram, and the obtained dark field sinogram.
9. The non-transitory computer-readable medium of claim 8 , including instructions to cause the processor to collect the under-sampled object scan data in a randomized manner.
10. The non-transitory computer-readable medium of claim 8 , including instructions to cause the processor to obtain the Fourier coefficients representative of the one or more PCT system contributions by performing an air scan.
11. The non-transitory computer-readable medium of claim 8 , including instructions to cause the processor to correct the computed Fourier coefficients for PCT system non-homogeneities during the dividing step.
12. The non-transitory computer-readable medium of claim 8 , including instructions to cause the processor to perform the regularized Fourier analysis step by solving a minimization equation expressed as
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13. The non-transitory computer-readable medium of claim 8 , including instructions to cause the processor to combine the regularized Fourier analysis step and the correcting step.
14. The non-transitory computer-readable medium of claim 13 , including instructions to cause the processor to perform the regularized Fourier analysis step by solving a minimization equation expressed as
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15. A phase contrast computed tomography (PCT) system comprising:
an x-ray emitting tube positioned to emit x-rays towards a scan subject;
a phase/absorption grating window on a side of the scan subject distal from the x-ray emitting tube;
an absorption window distal from the phase/absorption window;
an x-ray detector distal from the absorption window;
a control processor configured to execute computer instructions to cause the processor to perform a method for reconstructing under-sampled phase contrast computed tomography data, the method including:
obtaining under-sampled scan data of a subject-under-test, the object scan performed on a phase contrast computed tomography (PCT) system;
performing a regularized Fourier analysis on the under-sampled scan data;
computing Fourier coefficients for the under-sampled scan data;
correcting for one or more PCT system contributions to the under-sampled scan data by dividing the computed Fourier coefficients by Fourier coefficients representative of the one or more PCT system contributions;
obtaining at least one of an absorption sinogram, a differential phase sinogram, and a dark field sinogram from the corrected Fourier coefficients; and
performing tomographic reconstruction on the obtained absorption sinogram, the obtained differential phase sinogram, and the obtained dark field sinogram.
16. The system of claim 15 , including a regularizer unit configured to convert the reconstruction method from a local pixel-by-pixel task to a global task by exploiting prior knowledge from measured or synthetic data of at least one of neighboring detector pixels, and measured or synthetic data from neighboring view angles.
17. The system of claim 15 , including computer instructions to cause the control processor to collect the under-sampled object scan data in a randomized manner.
18. The system of claim 15 , including instructions to cause the control processor to perform the regularized Fourier analysis step by solving a minimization equation expressed as
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a
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-
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+
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(
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.
19. The system of claim 15 , including instructions to cause the processor to combine the regularized Fourier analysis step and the correcting step.
20. The system of claim 19 , including instructions to cause the control processor to perform the regularized Fourier analysis step by solving a minimization equation expressed as
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.