Interior SPECT - Exact and stable ROI reconstruction from uniformly attenuated local projections

Communications in Numerical Methods in Engineering

Volumn 25, Issue 6, 2009, Pages 693-710

  Yu, Hengyong ^a   Yang, Jiansheng ^b   Jiang, Ming ^b   Wang, Ge ^a  

^a Medical Center Boulevard   (United States)

^b PEKING UNIVERSITY   (China)

Author keywords

Analytic continuation; Exact interior reconstruction; Generalized Hilbert transform; Interior reconstruction; Single photon emission computed tomography (SPECT); Singular value decomposition (SVD)

Indexed keywords

ANALYTIC CONTINUATION; EXACT INTERIOR RECONSTRUCTION; GENERALIZED HILBERT TRANSFORM; INTERIOR RECONSTRUCTION; SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY (SPECT); SINGULAR VALUE DECOMPOSITION (SVD);

COMPUTER SIMULATION LANGUAGES; COMPUTERIZED TOMOGRAPHY; MATHEMATICAL TRANSFORMATIONS; MEDICAL IMAGING; PARTICLE BEAMS; PHOTONS; REPAIR; SINGULAR VALUE DECOMPOSITION;

SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY;

EID: 68149172849     PISSN: 10698299     EISSN: 10990887     Source Type: Journal    
DOI: 10.1002/cnm.1206     Document Type: Article

References (24)

1. Noo F, Clackdoyle R, Pack JD. A two-step Hilbert transform method for 2D image reconstruction. Physics in Medicine and Biology 2004; 49(17):3903-3923.
2. Defrise M et al. Truncated Hilbert transform and image reconstruction from limited tomographic data. Inverse Problems 2006; 22(3):1037-1053.
3. Wang G, Ye YB, Yu HY. General VOI/ROI reconstruction methods and systems using a truncated Hilbert transform (Patent disclosure submitted to Virginia Tech. Intellectual Properties on 15 May 2007), 2007.
4. Ye YB, Yu HY, Wei YC, Wang G. A general local reconstruction approach based on a truncated Hilbert transform. International Journal of Biomedical Imaging 2007; 2007:8. Article ID: 63634.
5. Ye YB, Yu HY, Wang G. Exact interior reconstruction with cone-beam CT. International Journal of Biomedical Imaging 2007; 2007:5. Article ID: 10693.
6. Ye YB, Yu HY, Wang G. Exact interior reconstruction from truncated limited-angle projection data. International Journal of Biomedical Imaging 2008; 2008:6. Article ID: 427989.
7. Natterer F. The mathematics of computerized tomography. Classics in Applied Mathematics. Society for Industrial and Applied Mathematics: Philadelphia, 2001.
8. Kudo H et al. Tiny a priori knowledge solves the interior problem. 2007 IEEE Nuclear Science Symposium and Medical Imaging, Honolulu, Hawaii, 28 October-3 November 2007; 4068-4075. Paper No.: M21-1.
9. Kudo H et al. Tiny a priori knowledge solves the interior problem in computed tomography. Physics in Medicine and Biology 2008; 53(9):2207-2231.
10. Li T et al. An efficient reconstruction method for nonuniform attenuation compensation in nonparallel beam geometries based on Novikov's explicit inversion formula. IEEE Transactions on Medical Imaging 2005; 24(10):1357-1368.
11. Tang QL et al. Exact fan-beam and 4 pi-acquisition cone-beam SPECT algorithms with uniform attenuation correction. Medical Physics 2005; 32(11):3440-3447.
12. Tang QL, Zeng GSL, Gullberg GT. Analytical fan-beam and cone-beam reconstruction algorithms with uniform attenuation correction for SPECT. Physics in Medicine and Biology 2005; 50(13):3153-3170.
13. Noo F et al. Image reconstruction from truncated data in single-photon emission computed tomography with uniform attenuation. Inverse Problems 2007; 23(2)645-667.
14. Rullgard H. An explicit inversion formula for the exponential Radon transform using data from 180 degrees. Arkiv för Matematik 2004; 42:353-362.
15. Rullgard H. Stability of the inverse problem for the attenuated Radon transform with 180 degrees data. Inverse Problems 2004; 20(3):781-797.
16. Courdurier M. Restricted measurements for the X-ray transform. Doctoral Dissertation, University of Washington, Seattle, 2007.
17. Nevanlinna R (ed.). Eindentige Analytische Functionen (2nd edn). Grundlehren der mathematischen Wissenschaften, vol. 46. Springer: Berlin, 1953.
18. Yu HY, Wang G. Studies on implementation of the Katsevich algorithm for spiral cone-beam CT. Journal of X-ray Science and Technology 2004; 12(2):96-117.
19. Hansen PC. Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank. SIAM Journal on Scientific and Statistical Computing 1990; 11(3):503-518.
20. Hansen PC. Regularization, GSVD and truncated GSVD. BIT 1989; 29(3):491-504.
21. Ramachandran PA. Method of fundamental solutions: singular value decomposition analysis. Communications in Numerical Methods in Engineering 2002; 18(11):789-801.
22. Ye YB, Zhao SY, Yu HY, Wang G. Exact reconstruction for cone-beam scanning along nonstandard spirals and other curves. Developments in X-Ray Tomography IV, Proceedings of SPIE, Denver, CO, U.S.A., vol. 5535, 4-6 August 2004; 293-300.
23. Ye YB, Zhao SY, Yu HY, Wang G. A general exact reconstruction for cone-beam CT via backprojection-filtration. IEEE Transactions on Medical Imaging 2005; 24(9):1190-1198.
24. Natterer F, Wubbeling F (eds). Mathematical Methods in Image Reconstruction. Society for Industrial and Applied Mathematics: Philadelphia, 2001.