Bayesian Reconstructions From Emission Tomography Data Using a Modified EM Algorithm

IEEE Transactions on Medical Imaging

Volumn 9, Issue 1, 1990, Pages 84-93

  Green, Peter J ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

IMAGE PROCESSING--RECONSTRUCTION; PROBABILITY--RANDOM PROCESSES;

BAYESIAN RECONSTRUCTIONS; EMISSION TOMOGRAPHY; EXPECTATION-MAXIMIZATION ALGORITHM; MAXIMUM LIKELIHOOD RECONSTRUCTION;

BIOMEDICAL ENGINEERING;

EID: 0025404969     PISSN: 02780062     EISSN: 1558254X     Source Type: Journal    
DOI: 10.1109/42.52985     Document Type: Article

References (31)

1. J. Besag, “Discussion of paper by P. Switzer,” Bull. Int. Stat. Inst., vol. L-3, pp. 422–425, 1983.
2. —, “On the statistical analysis of dirty pictures (with discussion),” J. Roy. Statist. Soc., B, vol. 48, pp. 259–302, 1986.
3. A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm (with discussion),” J. Roy. Statist. Soc., B, vol. 39, pp. 1–38, 1977.
4. C. E. Floyd, R. J. Jaszczak, and R. E. Coleman, “Inverse Monte-Carlo: A unified reconstruction algorithm for SPECT,” IEEE Trans. Nucl. Sci., vol. NS-32, pp. 779–785, 1985.
5. S. Geman and D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,” IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 721–741, 1984.
6. S. Geman and D. E. McClure, “Bayesian image analysis: An application to single photon emission tomography,” in Proc. Amer. Statist. Assoc., Stat. Comp., 1985, sect., 12–18.
7. —, “Statistical methods for tomographic image reconstruction,” ISI Tokyo session. Bull. Int. Stat. Inst., vol. LII-4, pp. 5–21, 1987.
8. I. J. Good and R. A. Gaskins, “Non-parametric roughness penalties for probability densities,” Biometrika, vol. 58, pp. 255–277.
9. P. J. Green, “Statistical methods for spatial image analysis,” Invited discussion contribution, ISI Tokyo session. Bull. Int. Stat. Inst., vol. LII-4, pp. 43–44, 1987.
10. —, “On use of the EM algorithm for penalized likelihood estimation,” J. Roy. Statist. Soc. B, 1990.
11. R. J. Jaszczak, R. E. Coleman, and C. B. Lim, “SPECT: Single photon emission computed tomography,” IEEE Trans. Nucl. Sci., vol. NS-27, pp. 1137–1153, 1980.
12. I. M. Johnstone and B. W. Silverman, “Speed of estimation in positron emission tomography,” Ann. Statist., to be published.
13. L. Kaufman, “Implementing and accelerating the EM algorithm for positron emission tomography,” IEEE Trans. Med. Imaging, vol. MI-6, pp. 37–51, 1987.
14. K. J. Kearfott, “Comment on paper by Vardi, Shepp and Kaufman,” J. Amer. Statist. Assoc., vol. 80, pp. 26–28, 1985.
15. K. Lange, M. Bahn, and R. Little, “A theoretical study of some maximum likelihood algorithms for emission and transmission tomography,” IEEE Trans. Med. Imaging, vol. MI-6, pp. 106–114, 1987.
16. S. A. Larsson, “Gamma camera emission tomography,” Acta Ra-diologica, Supplementum 363, Stockholm.
17. E. Levitan and G. T. Herman, “A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography,” IEEE Trans. Med. Imaging, vol. MI-6, pp. 185–192.
18. R. M. Lewitt and G. Muehllehner, “Accelerated iterative reconstruction for positron emission tomography based on the EM algorithm for maximum likelihood estimation,” IEEE Trans. Med. Imaging, vol. MI-5, pp. 16–22, 1986.
19. Z. Liang and H. Hart, “Bayesian image processing of data from constrained source distributions: I and II,” Bull. Math. Biol., vol. 49, pp. 51–91.
20. J. A. Neider and R. W. M. Wedderburn, “Generalized linear models,” J. Roy. Statist. Soc., A, vol. 135, pp. 370–384.
21. D. Nychka, “Some properties of adding a smoothing step to the EM algorithm,” Statist. Probabil. Lett., vol. 7, 1990.
22. B. C. Peters and H. F. Walker, “An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions,” SIAM J. Appl. Math., vol. 35, pp. 362–378, 1978.
23. L. A. Shepp and R. J. Vanderbei, “New insights into emission tomography via linear programming,” presented at NATO Meet, on Formation, Handling and Evaluation of Medical Images, Portugal, Sept. 1988.
24. L. A. Shepp and Y. Vardi, “Maximum likelihood reconstruction in positron emission tomography,” IEEE Trans. Med. Imaging, vol. MM, pp. 113–122, 1982.
25. B. W. Silverman, M. C. Jones, J. D. Wilson, and D. W. Nychka, “A smoothed EM approach to indirect estimation problems with particular reference to stereology and emission tomography,” J. Roy. Statist. Soc., B, 1990.
26. 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. Sci., vol. NS-32, pp. 3864–3872, 1985.
27. E. Tanaka, “A fast reconstruction algorithm for stationary positron emission tomography based on a modified EM algorithm,” IEEE Trans. Med. Imaging, vol. MI-6, pp. 98–105, 1987.
28. Y. Vardi, L. A. Shepp, and L. Kaufman, “A statistical model for positron emission tomography (with discussion),” J. Amer. Statist. Assoc., vol. 80, pp. 8–37, 1985.
29. E. Veklerov and J. Llacer, “Stopping rule for the MLE algorithm based on statistical hypothesis testing,” IEEE Trans. Med. Imaging, vol. MI-6, pp. 313–319, 1987.
30. E. Veklerov, J. Llacer, and E. J. Hoffman, “MLE reconstruction of a brain phantom using a Monte-Carlo transition matrix and a statistical stopping rule,” IEEE Trans. Nucl. Sci., vol. NS-35, pp. 603–607, 1988.
31. K. Lange and R. Carson, “EM reconstruction algorithms for emission and transmission tomography,” J. Comput. Assist. Tomog., vol. 8, pp. 306–316, 1984.