Convergence of EM Image Reconstruction Algorithms with Gibbs Smoothing

IEEE Transactions on Medical Imaging

Volumn 9, Issue 4, 1990, Pages 439-446

  Lange, Kenneth ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTERIZED TOMOGRAPHY - MATHEMATICAL MODELS; IMAGE PROCESSING - RECONSTRUCTION; MATHEMATICAL TECHNIQUES - ALGORITHMS;

GIBBS SMOOTHING; MEDICAL IMAGING; TRANSMISSION TOMOGRAPHY;

IMAGING TECHNIQUES;

EID: 0025587714     PISSN: 02780062     EISSN: 1558254X     Source Type: Journal    
DOI: 10.1109/42.61759     Document Type: Article

References (24)

1. L. A. Shepp and Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imaging, vol. 1, pp. 113– 121, 1982.
2. K. Lange and R. Carson, “EM reconstruction algorithms for emission and transmission tomography,” J. Comput. Assist. Tomog., vol. 8, pp. 306–316, 1984.
3. Y. Vardi, L. A. Shepp, and L. Kaufman, “A statistical model for positron emission tomography,” J. Amer. Statist. Assoc., vol. 80, pp. 8–37, 1985.
4. M. Defrise, “Possible criteria for choosing the number of iterations in some iterative reconstruction methods,” in Proc. NATO Advanced Summer Inst, on Math. Comput. Sci. in Med. Imaging, El Ciocco, Italy, 1986.
5. T. Hebert, R. Leahy, and M. Singh, “Fast MLE for SPECT using an intermediate polar representation and a stopping criterion,” IEEE Trans. Nucl. Sci., vol. NS-35, Feb. 1988.
6. J. Llacer and E. Veklerov, “Feasible images and practical stopping rules for iterative algorithms in emission tomography,” IEEE Trans. Med. Imaging, vol. 8, pp. 186–193, 1989.
7. S. Geman and D. McClure, “Bayesian image analysis: An application to single photon emission tomography,” in Proc. Statist. Comput. Sect., Amer. Statist. Assoc., Washington D.C, pp. 12–18, 1985.
8. —, “Statistical methods for tomographic image reconstruction. 1SI Tokyo session,” Bull. Int. Statist. Inst., vol. LI1-4. pp. 5–21. 1987.
9. T. Hebert and R. Leahy, “A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors,” IEEE Trans. Med. Imaging, vol. 8, pp. 194–202, 1989.
10. P. J. Green, “Bayesian reconstructions from emission tomography data using a modified EM algorithm,”
11. S. Geman and D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,” IEEE Trans. Putt. Anal. Machine Intell., vol. PAMI-6, pp. 721–741, 1984.
12. J. Besag, “On the statistical analysis of dirty pictures,” J. Royal Statist. Soc, B, vol. 48, pp. 259–302, 1986.
13. 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. 6, pp. 106–114, 1987.
14. P.J. Green, “On the use of the EM algorithm for penalized likelihood estimation.
15. C. F. J. Wu, “On the convergence properties of the EM algorithm,” Ann. Statist., vol. 11, pp. 95–103, 1983.
16. A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. Royal Statist. Soc, B, vol. 39, pp. 1–38, 1977.
17. K. Manbeck, “Bayesian Statistical Methods Applied to Emission Tomography with Physical Phantom and Patient Data,” Ph.D. dissertation. Division of Applied Mathematics, Brown University, Providence. RI 1990.
18. M. Almedia and B. Gidas, “A Variational Method for Estimating the Parameters of MRF from Complete or Incomplete Data,” Preprint, Brown University, 1989.
19. L. Kaufman, “Implementing and accelerating the EM algorithm for positron emission tomography,” IEEE Trans. Med. Imaging, vol. 6, pp. 37–51, 1987.
20. D. G. Luenberger, Linear and Nonlinear Programming, 2nd ed. Reading, Massachusetts: Addison-Wesley, 1984.
21. J. M. Ortega and W. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables. New York: Academic, 1970.
22. A. M. Ostrowski. Solutions of Equations in Euclidean and Banach Spaces. New York: Academic. 1973, p. 173.
23. E. J. Beltrami. An Algorithmic Approach to Nonlinear Analysis and Optimization. New York: Academic, 1970.
24. C. A. Pelizzari. G. T. Y. Chen, D. R. Spelbring, R. R. Weichselbaum, and C-T. Chen, “Accurate three-dimensional registration of CT. PET, and/or MR images of the brain,” J. Comput. Assist. Tomography, vol. 13, pp. 20–26. 1989.