Generalized matrix inverse reconstruction for SPECT using a weighted singular value spectrum

IEEE Transactions on Nuclear Science

Volumn 43, Issue 3 PART 2, 1996, Pages 2008-2017

  Smith, Mark F ^a,b  

^a Duke University   (United States)

^b DUKE UNIVERSITY MEDICAL CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; COMPUTERIZED TOMOGRAPHY; INVERSE PROBLEMS; MATRIX ALGEBRA; MEDICAL IMAGING; MONTE CARLO METHODS; NUCLEAR MEDICINE;

CLINICAL SCANNER; GENERALIZED MATRIX INVERSE; MYOCARDIAL PERFUSION; RESOLUTION KERNEL; SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY; SPECT IMAGE RECONSTRUCTION; SPECTRAL WEIGHTS; TRUNCATED SPECTRUM; VOXEL; WEIGHTED SINGULAR VALUE SPECTRUM;

IMAGE RECONSTRUCTION;

EID: 0030168859     PISSN: 00189499     EISSN: None     Source Type: Journal    
DOI: 10.1109/23.507261     Document Type: Article

References (46)

1. T. F. Budinger and G. T. Gullberg, "Three dimensional reconstruction in nuclear medicine emission imaging," IEEE Trans. Nucl. Sci., vol. NS-21, pp. 2-20, 1974.
2. L. A. Shepp and Y. Vardi, "Maximum likelihood reconstruction for emission tomography," IEEE Trans. Med. Imaging, vol. MI-1, pp. 113-122, 1982.
3. G. L. Zeng, G. T. Gullberg, B. M. W. Tsui and J. A. Terry, "Three-dimensional iterative reconstruction algorithms with attenuation and geometric point response correction," IEEE Trans. Nucl. Sci., vol. 38, pp. 693-702, 1991.
4. L. A. Shepp and B. F. Logan, "The Fourier reconstruction of a head section," IEEE Trans. Nucl. Sci., vol. NS-21, pp. 2143, 1974.
5. R. H. Huesman, "A new fast algorithm for the evaluation of regions of interest and statistical uncertainty in computed tomography," Phys. Med. Biol., vol. 29, pp. 543-552, 1984.
6. R. E. Carson, "A maximum likelihood method for region-of-interest evaluation in emission tomography," J. Assist. Comput. Tomogr., vol. 10, pp. 654-663, 1986.
7. C. R. Rao and S. K. Mitra, Generalized Inverse of Matrices and its Applications. New York: John Wiley & Sons, 1971.
8. A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications. New York: John Wiley & Sons, 1974.
9. C. W. Groetsch, Generalized Inverses of Linear Operators: Representation and Approximation. New York: Marcel Dekker, 1977.
10. [101 S. L. Campbell and C. D. Meyer, Jr., Generalized Inverses of Linear Transformations. London: Pitman, 1979.
11. M. Z. Nashed, editor, Generalized Inverses and Applications. New York: Academic Press, 1976.
12. P. C. Sabatier, "Basic concepts and methods of inverse problems," in Basic Methods of Tomography and Inverse Problems, P. C. Sabatier, Ed. Bristol: Adam Hilger, 1987, pp. 470-635.
13. M. Bertero, "Linear inverse and ill-posed problems," in Advances in Electronics and Electron Physics, vol. 75, P. W. Hawkes, Ed. Boston: Academic Press, 1989, pp. 1-120.
14. W. Menke, Geophysical Data Analysis: Discrete Inverse Theory, revised ed. San Diego: Academic Press, 1984.
15. M. Bertero, C. De Mol and E. R. Pike, "Linear inverse problems with discrete data: II. Stability and regularisation," Inverse Problems, vol. 4, pp. 573-594, 1988.
16. S. Twomey, "The application of numerical filtering to the solution of integral equations encountered in indirect sensing measurements," J. Franklin Inst., vol. 279, pp. 95-109, 1965.
17. I. J. D. Craig and J. C. Brown, Inverse Problems in Astronomy: A Guide to Inversion Strategies for Remotely Sensed Data. Bristol: Adam Hilger, 1986.
18. A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems. Washington, D.C.: V. H. Winston & Sons, 1977.
19. F. Natterer, The Mathematics of Computerized Tomography. Stuttgart and Chichester: B. G. Teubner and John Wiley & Sons, 1986.
20. P. C. Hansen, "Numerical tools for analysis and solution of Fredholm integral equations of the first kind," Inverse Problems, vol. 8, pp. 849-872, 1992.
21. H. C. Andrews and B. R. Hunt, Digital Image Restoration. Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1977.
22. B. R. Frieden, "Image enhancement and restoration," in Picture Processing and Digital Filtering, T. S. Huang, Ed., 2nd ed. Berlin: Springer-Verlag, 1979.
23. W. K. Pratt, Digital Image Processing, New York: Wiley-Interscience, 1991.
24. K. Aki and P. G. Richards, Quantitative Seismology, vol. II. San Francisco: W. H. Freeman, 1980.
25. A. F. Bennett, Inverse Methods in Oceanography. Cambridge, England: Cambridge University Press, 1992.
26. N.-Z. Sun, Inverse Problems in Groundwater Modeling. Dordrecht: Kluwer, 1994.
27. J. V. Beck, B. Blackwell and C. R. St. Clair, Jr., Inverse Heat Conduction: Ill-Posed Problems. New York: WileyInterscience, 1985.
28. J. N. Franklin, "Well-posed stochastic extensions of ill-posed linear problems," J. Math. Anal. Appl., vol. 31, pp. 682-716, 1970.
29. Y. S. Shim and Z. H. Cho, "SVD pseudoinversion image reconstruction," IEEE Trans. ASSP, vol. ASSP-29, pp. 904-909, 1981.
30. P. Hughett, "An optimal constrained linear inverse method for magnetic source imaging," Annals Biom. Eng., vol. 23, pp. 506-523, 1995.
31. U. Raff, D. N. Stroud and W. R. Hendee, "Improvement of lesion detection in scintigraphic images by SVD techniques for resolution recovery," IEEE Trans. Med. Imaging, vol. MI-5, pp. 35-44, 1986.
32. R. M. Lewitt, G. Muehllehner and J. S. Karp, "Three-dimensional image reconstruction for PET by multi-slice rebinning and axial image filtering," Phys. Med. Biol., vol. 39, pp. 321-339, 1994.
33. J. Llacer, "Theory of imaging with a very limited number of projections," IEEE Trans. Nucl. Sci., vol. NS-26, pp. 596-602, 1979.
34. J. Llacer, "Tomographic image reconstruction by eigenvector decomposition: its limits and areas of applicability," IEEE Trans. Med. Imaging, vol. MI-1, pp. 34-42, 1982.
35. J. Llacer and J. D. Meng, "Matrix-based image reconstruction methods for tomography," IEEE Trans. Nucl. Sci., vol. NS-32, pp. 855-864, 1985.
36. H. H. Barrett, J. N. Aarsvold and T. J. Roney, "Null functions and eigenfunctions: tools for the analysis of imaging systems," in Information Processing in Medical Imaging, D. A. Ortendahl and J. Llacer, Eds. Berkeley, California: Wiley-Liss, 1991, pp. 211-226.
37. G. T. Gullberg, R. H. Huesman, G. L. Zeng and A. M. Smith, "Efficient estimation of dynamic cardiac SPECT kinetic parameters using singular value decomposition reconstruction [Abstract]," J. Nucl. Med., vol. 35, pp. 18P, 1994.
38. M. F. Smith, C. E. Floyd, Jr, R. J. Jaszczak and R. E. Coleman, "Reconstruction of SPECT images using generalized matrix inverses," IEEE Trans. Med. Imaging, vol. 11, pp. 165-175, 1992.
39. M. F. Smith and R. J. Jaszczak, "Simultaneously constraining SPECT activity estimates with primary and secondary energy window projection data," IEEE Trans. Med. Imaging, vol. 13, pp. 329-337, 1994.
40. M. F. Smith, C. E, Floyd, Jr, R. J. Jaszczak and R. E. Coleman, "Evaluation of projection pixel-dependent and pixel-independent scatter correction in SPECT," IEEE Trans. Nucl. Sci., vol. 39, pp. 1099-1105, 1992.
41. M. F. Smith and R. J. Jaszczak, "Generalized dual-energy-window scatter compensation in spatially varying media for SPECT," Phys. Med. Biol., vol. 39, pp. 531-546, 1994.
42. R. A. Wiggins, "The general linear inverse problem: implication of surface waves and free oscillations for earth structure," Rev. Geophys. Space Phys., vol. 10, pp. 251-285, 1972.
43. G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd ed. Baltimore: The Johns Hopkins University Press, 1989.
44. G. Backus and F. Gilbert, "The resolving power of gross earth data," Geophys. J. R. Astr. Soc., vol. 16, pp. 169-205, 1968.
45. M. F. Smith, C. E. Floyd, Jr and R. J. Jaszczak, "A vectorized Monte Carlo code for modeling photon transport in SPECT," Med. Phys., vol. 20, pp. 1121-1127, 1993.
46. R. J. Jaszczak, K. L. Greer, C. E. Floyd, Jr., C. C. Harris and R. E. Coleman, "Improved SPECT quantification using compensation for scattered photons," J. Nucl. Med., vol. 25, pp. 893-900, 1984.