Penalized Maximum-Likelihood Image Reconstruction Using Space-Alternating Generalized EM Algorithms

IEEE Transactions on Image Processing

Volumn 4, Issue 10, 1995, Pages 1417-1429

  Fessler, Jeffrey A ^a   Hero, Alfred O ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; IMAGE QUALITY; NUMERICAL ANALYSIS; SPURIOUS SIGNAL NOISE; STATISTICAL METHODS;

EXPECTATION MAXIMIZATION (EM) ALGORITHM; MAXIMUM LIKELIHOOD IMAGE RECONSTRUCTION; SPACE ALTERNATING GENERALIZED EM ALGORITHM;

IMAGE RECONSTRUCTION;

EID: 0029392038     PISSN: 10577149     EISSN: 19410042     Source Type: Journal    
DOI: 10.1109/83.465106     Document Type: Article

References (53)

1. K. Lange and R. Carson, “EM reconstruction algorithms for emission and transmission tomography,” J. Comp. Assisted Tomo., vol. 8, no. 2, pp. 306-316, Apr. 1984.
2. S. Joshi and M. I. Miller, “Maximum a posteriori estimation with good's roughness for three-dimensional optical-sectioning microscopy,” J. Opt. Soc. Am. Ser. A, vol. 10, no. 5, pp. 1078-1085, May 1993.
3. D. L. Snyder, A. M. Hammoud, and R. L. White, “Image recovery from data acquired with a charge-couple-device camera,” J. Opt. Soc. Am. Ser. A, vol. 10, no. 5, pp. 1014-1023, May 1993.
4. A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. Royal Stat. Soc. Ser. B. vol. 39, no. 1, pp. 1-38, 1977.
5. D. G. Politte and D. L. Snyder, “Corrections for accidental coincidences and attenuation in maximum-likelihood image reconstruction for positron-emission tomography,” IEEE Trans. Med. Imaging, vol. 10, no. 1, pp. 82-89, Mar. 1991.
6. M. E. Daube-Witherspoon, R. E. Carson, Y. Yan, and T. K. Yap, “Scatter correction in maximum likelihood reconstruction of PET data,” in Conf Rec. IEEE Nucl. Sci. Symp. Med. Imaging Conf, 1992, pp. 945-947.
7. R. Molina and B. D. Ripley, “Deconvolution in optical astronomy. A Bayesian approach,” in Stochastic Models, Statistical Methods, and Algorithms in Im. Analysis, P. Barone, A. Frigessi, and M. Piccioni, Eds., Lecture Notes in Statistics. New York: Springer, 1992, vol. 74, pp. 233-239.
8. J. A. Fessler and A. O. Hero, “Complete-data spaces and generalized EM algorithms,” in Proc. IEEE Conf. Acoust., Speech, Signal Processing, vol. 4, 1993, pp. 1-4.
9. “Space-alternating generalized expectation-maximization algorithm,” IEEE Trans. Signal Processing, vol. 42, no. 10, pp. 2664-2677, Oct. 1994.
10. J. A. Fessler, “Hidden data spaces for maximum-likelihood PET reconstruction,” in Conf Rec. IEEE Nucl. Sci. Symp. Med. Imaging Conf., vol. 2, 1992, pp. 898-900.
11. J. A. Fessler, N. H. Clinthorne and W. L. Rogers, “On complete data spaces for PET reconstruction algorithms,” IEEE Trans. Nucl. Sci., vol. 40, no. 4, pp. 1055-1061, Aug. 1993.
12. J. A. Fessler and A. O. Hero, New complete-data spaces and faster algorithms for penalized-likelihood emission tomography,” in Conf. Rec. IEEE Nucl. Sci. Symp. Med. Imaging Conf., 1993, pp. 1897-1901.
13. A. O. Hero and J. A. Fessler, “Asymptotic convergence properties of EM-type algorithms,” Commun. Signal Processing Lab., Dept. of EECS, Univ. of Michigan, Ann Arbor, MI, Tech. Rep. 282, Apr. 1993.
14. “Convergence in norm for alternating expectation-maximization (EM)-type algorithms,” Statistica Sinica, vol. 5, no. 1, pp. 41-54, Jan. 1995
15. E. Veklerov and J. Llacer, “Stopping rule for the MLE algorithm based on statistical hypothesis testing,” IEEE Trans. Med. Imaging, vol. 6, no. 4, pp. 313-319, Dec. 1987.
16. J. A. Fessler, “Penalized weighted least-squares image reconstruction for positron emission tomography,” IEEE Trans. Med. Imaging, vol. 13, no. 2, pp. 290-300, June 1994.
17. 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, no. 2, pp. 106-114, June 1987.
18. E. M. Levitan and G. T. Herman, “A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography,” IEEE Trans. Med. Imaging, vol. 6, no. 3, pp. 185-192, Sept. 1987.
19. 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. Royal Stat. Soc. Ser. B, vol. 52, no. 2, pp. 271-324, 1990.
20. D. L. Snyder, M. I. Miller, L. J. Thomas, and D. G. Politte, “Noise and edge artifacts in maximum-likelihood reconstructions for emission tomography,” IEEE Trans. Med. Imaging, vol. 6, no. 3, pp. 228-238, Sept. 1987.
21. C. S. Butler and M. I. Miller, “Maximum a posteriori estimation for SPECT using regularization techniques on massively parallel computers,” IEEE Trans. Med. Imaging, vol. 12, no. 1, pp. 84-89, Mar. 1993.
22. 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, no. 2, pp. 194-202, June 1989.
23. X. L. Meng and D. B. Rubin, “Maximum likelihood estimation via the ECM algorithm: A general framework,” Biometrika, vol. 80, no. 2, pp. 267-278, 1993.
24. C. H. Liu and D. B. Rubin, “The ECME algorithm: A simple extension of EM and ECM with faster monotone convergence,” Biometrika, vol. 81, no. 4, pp. 633-648, 1994.
25. A. R. De Pierro, “A generalization of the EM algorithm for maximum likelihood estimates from incomplete data,” Med. Im. Proc. Group, Dept. of Radiol. Univ. of Pennsylvania, Tech. Rep. MIPGl19. 1987.
26. “A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography,” IEEE Trans. Med. Imaging, vol. 14, no. 1, pp. 132-137, Mar. 1995.
27. M. Abdalla and J. W. Kay, “Edge-preserving image restoration,” in Stochastic Models, Statistical Methods, and Algorithms in Im. Analysis, P. Barone, A. Frigessi, and M. Piccioni, Eds., Lecture Notes in Statistics. New York: Springer, 1992, vol. 74, pp. 1-13.
28. S. Geman and D. E. McClure, “Bayesian image analysis: An application to single photon emission tomography,” in Proc. Stat. Comp. Sect. Am. Stat. Assoc., 1985, pp. 12-18.
29. “Statistical methods for tomographic image reconstruction,” in Proc. 46 Sect. ISI, Bull. ISI, vol. 52, 1987, pp. 5-21.
30. P. J. Green, “Bayesian reconstructions from emission tomography data using a modified EM algorithm,” IEEE Trans. Med. Imaging, vol. 9, no. I, pp. 84-93, Mar. 1990.
31. “Statistical methods for spatial image analysis (discussion),” in Proc. 46 Sect. ISI, Bull. ISI, vol. 52. 1987, pp. 43-44.
32. K. Lange, “Convergence of EM image reconstruction algorithms with Gibbs smoothing,” IEEE Trans. Med. Imaging, vol. 9, no. 4, pp. 439-446, Dec. 1990, Corrections, June 1991.
33. Z. Liang, R. Jaszczak, and K. Greer, “On Bayesian image reconstruction from projections: Uniform and nonuniform a priori source information,” IEEE Trans. Med. Imaging, vol. 8, no. 3, pp. 227-235, Sept. 1989.
34. G. T. Herman and D. Odhner, “Performance evaluation of an iterative image reconstruction algorithm for positron-emission tomography,” IEEE Trans. Med. Imaging, vol. 10, no. 3, pp. 336-346, Sept. 1991.
35. G. T. Herman, D. Odhner, K. D. Toennies, and S. A. Zenios, “A parallelized algorithm for image reconstruction from noisy projections,” in Large-Scale Numerical Optimization, T. F. Coleman and Y. Li, Eds. Philadelphia, PA: SIAM, 1990, pp. 3-21.
36. A. W. McCarthy and M. I. Miller, “Maximum likelihood SPECT in clinical computation times using mesh-connected parallel processors,” IEEE Trans. Med. Imaging, vol. 10, no. 3, pp. 426-436, Sept. 1991.
37. M. I. Miller and B. Roysam, “Bayesian image reconstruction for emission tomography incoporating Good's roughness prior on massively parallel processors,” in Proc. Nat. Acad. Sci., vol. 88, Apr. 1991, pp. 3223-3227.
38. A. D. Lantermann, “A new way to regularize maximum-likelihood estimates for emission tomography with Good's roughness penalty,” Elec. Sys. and Sig. Res. Lab., Washington Univ., Tech. Rep. ESSRL-92-05, 92-05, Jan. 1992.
39. D. L. Snyder, A. D. Lanterman, and M. I. Miller, “Regularizing images in emission tomography via an extension of Good's roughness measure,” Washington Univ., Tech. Rep. ESSRL-92-17, Jan. 1992.
40. C. Bouman and K. Sauer, “Fast numerical methods for emission and transmission tomographic reconstruction,” in Proc. 27th Conf. Inform. Sci. Syst., Johns Hopkins, 1993, pp. 611-616.
41. “A unified approach to statistical tomography using coordinate descent optimization,” IEEE Trans. Image Processing, to be published.
42. E. U. Mumcuoglu, R. Leahy, S. R. Cherry, and Z. Zhou, “Fast gradient-based based methods for Bayesian reconstruction of transmission and emission PET images,” Signal and Image Processing Inst., USC, Tech. Rep. 241, Sept. 1993.
43. J. A. Fessler and A. O. Hero, “Space-alternating generalized EM algorithms for penalized maximum-likelihood image reconstruction,” Comm. and Sign. Proc. Lab., Dept. of EECS, Univ. of Michigan, Ann Arbor, MI, Tech. Rep. 286, Feb. 1994.
44. A. R. De Pierro, “On the relation between the ISRA and the EM algorithm for positron emission tomography,” IEEE Trans. Med. Imaging, vol. 12, no. 2, pp. 328-333, June 1993.
45. L. Kaufman, “Implementing and accelerating the EM algorithm for positron emission tomography,” IEEE Trans. Med. Imaging, vol. 6, no. 1, pp. 37-51, Mar. 1987.
46. A. O. Hero and J. A. Fessler, “A recursive algorithm for computing Cramer-Rao-type bounds on estimator covariance,” IEEE Trans. Inform. Theory, vol. 40, no. 4, pp. 1205-1210, July 1994.
47. K. Sauer and C. Bouman, “A local update strategy for iterative reconstruction from projections,” IEEE Trans. Signal Processing, vol. 41, no. 2, pp. 534-548, Feb. 1993.
48. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C. Cambridge, MA: Cambridge Univ. Press, 1988.
49. H. M. Hudson and R. S. Larkin, “Acceleration image reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging, vol. 13, no. 4, pp. 601-609, Dec. 1994.
50. M. Rosenlicht, Introduction to Analysis. New York: Dover, 1985.
51. R. E. Williamson, R. H. Crowell, and H. F. Trotter, Calculus of Vector Functions. Englewood Cliffs, NJ: Prentice-Hall, 1972.
52. A. M. Ostrowski, Solution of Equations in Euclidian and Banach Spaces. New York: Academic, 1973.
53. T. M. Cover, “An algorithm for maximizing expected log investment return,” IEEE Trans. Inform. Theory, vol. 30, no. 2, pp. 369-373, Mar. 1984.