Image reconstruction in 2D SPECT with 180° acquisition

Inverse Problems

Volumn 17, Issue 5, 2001, Pages 1357-1371

  Noo, Frédéric ^a   Wagner, Jean Marc ^b  

^a UNIVERSITY OF UTAH SCHOOL OF MEDICINE   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035473378     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/17/5/308     Document Type: Article

References (26)

1. Novikov R G 2000 An inversion formula for the attenuated x-ray transformation Preprint CNRS, UMR 6629, Departement de mathematiques. Université de Nantes, France
2. Natterer F 2001 Inversion of the attenuated Radon transform Inverse Problems 17 113-9
3. Kunyansky L A 2001 A new SPECT reconstruction algorithm based on the Novikov explicit inversion formula Inverse Problems 17 293-306
4. Markoe A 1984 Fourier inversion of the attenuated x-ray transform SIAM J. Math. Anal. 15 718-22
5. Bellini S. Piacenti M, Caffario C and Rocca F 1979 Compensation of tissue absorption in emission tomography IEEE Trans. Acoust. Speech Signal Processing 27 213-8
6. Tretiak O and Metz C 1980 The exponential Radon transform SIAM J. Appl. Math. 39 341-54
7. Clough A and Barrett H H 1980 Attenuated Radon and Abel transforms J. Opt. Soc. Am. 39 341-54
8. Gullberg G T and Budinger T F 1981 The use of filtering methods to compensate for constant attenuation in single-photon emission computed tomography IEEE Trans. Biomed. Eng. 8 142-57
9. Finch D V and Hertle A 1987 The exponential Radon transform Intregral Geometry (Contemporary Mathematics, vol 63) ed Bryant, Guillemin, Helgason and Wells (Providence, RI: American Mathematical Society) pp 67-73
10. Hawkins W G, Leichner P K and Yang N C 1988 The circular harmonic transform for SPECT reconstruction and boundary conditions on the Fourier transform of the sinogram IEEE Trans. Med. Imaging 7 135-48
11. Inouye T, Kose K and Hasegawa A 1989 Image reconstruction algorithm for single-photon-emission computed tomography with uniform attenuation Phys. Med. Biol. 34 299-304
12. Hazou I A and Solmon D C 1988 Inversion of the exponential x-ray transform. I: analysis Math. Methods Appl. Sci. 10 561-74
13. Hazou I A and Solmon D C 1989 Filtered-backprojection and the exponential Radon transform J. Math. Anal. Appl. 141 109-19
14. Hazou I A and Solmon D C 1990 Inversion of the exponential x-ray transform. II: numerics Math. Methods Appl. Sci. 13 205-18
15. Gullberg G T and Zeng G L 1994 Reconstruction algorithm using singular value decomposition of a discrete representation of the exponential Radon transform using natural pixels IEEE Trans. Nucl. Sci. 41 2812-9
16. Liang Z, Ye J and Harrington D P 1994 An analytical approach to quantitative reconstruction of non-uniform attenuated brain SPECT Phys. Med. Biol. 39 2023-41
17. Metz C E and Pan X 1995 A unified analysis of exact methods of inverting the 2D exponential Radon transform, with implications for noise control in SPECT IEEE Trans. Med. Imaging 14
18. Pan X and Metz C E 1995 Analysis of noise properties of a class of exact methods of inverting the 2D exponential Radon transform IEEE Trans. Med. Imaging 14
19. Liang Z, Ye J, Cheng J and Harrington D P 1996 The inversion of the exponential Radon transform for quantitative brain SPECT Phys. Med. Biol. 41 1227-32
20. Weng Y, Zeng L and Gullberg G T 1997 Analytical Inversion formula for uniformly attenuated fan-beam projections IEEE Trans. Nucl. Sci. 44 243-9
21. You J, Liang Z and Zeng G L 1999 A unified reconstruction framework for both parallel-beam and variable focal-length fan-beam collimators by a Cormack-type inversion of exponential Radon transform IEEE. Trans. Med. Imaging 18 59-65
22. Clarkson E 1999 Projections onto the range of the exponential Radon transform and reconstruction algorithms Inverse Problems 15 563-71
23. Kuchment P and Shneiberg I 1994 Some inversion formulae in the single photon em ssion computed tomography Appl. Anal. 53 221-31
24. Palamodov V P 1996 An inversion method for an attenuated x-ray transform Inverse Problems 12 717-29
25. Kreyszig E 1989 Introductory Functional Analysis with Applications (New York: Wiley)
26. Johnson L W and Riess R D 1977 Numerical Analysis (Reading, MA: Addison-Wesley)