An SVD Reconstruction algorithm using a natural pixel representation of the attenuated radon transform

IEEE Transactions on Nuclear Science

Volumn 43, Issue 1 PART 2, 1996, Pages 295-303

  Gullberg, Grant T ^a,b   Hsieh, Yu Lung ^a,b   Larry Zeng, G ^a,b  

^a IEEE   (United States)

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

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ATTENUATION; CALCULATIONS; COMPUTER SIMULATION; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS;

ATTENUATED RADON TRANSFORM; ATTENUATION CORRECTION; BACKPROJECTION; EMISSION DATA; NATURAL PIXELS; PIXEL REPRESENTATION; SINGULAR VALUE DECOMPOSITION;

IMAGE RECONSTRUCTION;

EID: 0030086234     PISSN: 00189499     EISSN: None     Source Type: Journal    
DOI: 10.1109/23.485969     Document Type: Article

References (24)

1. G. L. Zeng and G. T. Gullberg, An itérative reconstruction algorithm with natural pixel basis, J. Nucl. Med., vol. 34, p. 19P, 1993.
2. G. T. Gullberg and G. L. Zeng, A reconstruction algorithm using singular value decomposition of a discrete representation of the exponential Radon transform using natural pixels, IEEE Trans. Nucl. Sei., vol. 41, pp. 2812-2819, 1994.
3. O. J. Tretiak and C. Metz, The exponential Radon transform, SIAM J. Appl. Math, vol. 39, pp. 341-354, 1980. .
4. G. T. Gullberg and T. F. Budinger, The use of filtering methods to compensate for constant attenuation in single-photon emission computed tomography, IEEE Trans. Biomed Eng., vol. BME-28, pp. 142-157, 1981.
5. G. T. Gullberg, The attenuated radon transform: Theory and application in medicine and biology, Ph.D. thesis, University of California at Berkeley, 1979.
6. F. Natterer, The Mathematics of Computerized Tomography. Chichester, U.K: Wiley, 1986, pp. 144-150 and 156-157.
7. F. Natterer, Efficient implementation of optimal algorithms in computerized tomography, Math. Meths. In Appl, Sei., vol. 2, pp. 545-555, 1980.
8. M. H. Buonocore, W. R. Brody, and A. Macovski, A natural pixel decomposition for two-dimensional image reconstruction, IEEE Trans. Biomed. Eng., vol. BME-28, pp. 69-78, 1981.
9. G. Backus and F. Gilbert, The resolving power of gross earth data, Geophys. J. R. Astr. Hoc., vol. 16, pp. 169-205, 1968.
10. M. Bertero, C. De Mol, and E. R. Pike, Linear inverse problems with discrete data. I: General formulation and singular system analysis, Inverse Problems, vol. 1, pp. 301-330, 1985.
11. Linear inverse problems with discrete data: II. Stability and régularisation, Inverse Problems, vol. 4, pp. 573-594, 1988.
12. L. Garnero, J.-P. Hugonin, and N. De Beaucoudrey, Limited-angle tomographic imaging using a constrained natural-pixel decomposition, Optica Acta, vol. 33, pp. 659-671, 1986.
13. J. R. Baker, Spatially variant tomographic imaging: Estimation, identification, and optimization, Ph.D. dissertation, University of California at Berkeley, 1991.
14. J. R. Baker, T. F. Budinger, and R. H. Huesman, Generalized approach to inverse problems in tomography: Image reconstruction for spatially variant systems using natural pixels, Critical Rev. Biomed. Eng., vol. 20, pp. 47-71, 1992.
15. D. L. Snyder and M. I. Miller, The use of sieves to stabilize images produced with the EM algorithm for emission tomography, IEEE Trans. Nucl. Sei., vol. NS-32, pp. 3864-3872, 1985.
16. E. Levitan and G. T. Herman, A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography, IEEE Trans. Med. Imag., vol. MI-6, pp. 185-192, 1987.
17. D. S. Lalush and B. M. W. Tsui. Simulation evaluation of Gibbs prior distributions for use in maximum a posteriori SPECT reconstructions, IEEE Trans. Med. Imag., vol. 11, pp. 267-275, 1992.
18. G. T. Gullberg, R. H. Huesman, J. A. Malko, N. J. Pelc, and T. F. Budinger, An attenuated projector-backprojector for iterative SPECT reconstruction, Phys. Med. Blol, vol. 30, pp 799-816, 1985.
19. R. H. Huesman, G. T. Gullberg, W. L. Greenberg, and T. F. Budinger, Donner Algorithms for Reconstruction Tomography, Lawrence Laboratory Pub. PUB 214, 1977.
20. K. M. Hanson and G. W. Wecksung, Local basis-function approach to computed tomography, Appl. Optics, vol.. 24, pp. 4028-1-039, 1985.
21. R. M. Lewitt, Alternatives to voxels for image representation in iterative reconstruction algorithms, Phys. Med. Biol, vol. 37, pp. 705-716, 1992.
22. M. H. Buonocore, W. R. Brody, A. Macovski, and S. L. Wood, A polar pixel Kaiman filter for limited data CT image reconstruction, in Proc. Soc. Photo-Opt. Instrum. Eng., San Diego, CA, Aug. 1979, vol. 206, pp. 109-115.
23. C. E. Floyd, R. J. Jaszczak, and R. E. Coleman, Image resampling on a cylindrical sector grid, IEEE Trans. Med. Imag., vol. MI-5, pp. 128-131, 1986.
24. T. J. Hebert and R. M. Leahy, Fast methods for including attenuation in the EM algorithm, IEEE Trans. Nucl. Sei., vol. 37, pp. 754-758, 1990.