A Generalized Gaussian Image Model for Edge-Preserving MAP Estimation

IEEE Transactions on Image Processing

Volumn 2, Issue 3, 1993, Pages 296-310

  Bouman, Charles ^a   Sauer, Ken ^b  

^a PURDUE UNIVERSITY   (United States)

^b UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER VISION; IMAGE RECONSTRUCTION; MATHEMATICAL MODELS; PARAMETER ESTIMATION; ROBUSTNESS (CONTROL SYSTEMS); SIGNAL FILTERING AND PREDICTION; STATISTICAL METHODS;

A POSTERIORI LOG-LIKELIHOOD FUNCTION; EDGE PRESERVING MAP ESTIMATION; GENERALIZED GAUSSIAN MARKOV RANDOM FIELD;

IMAGE PROCESSING;

EID: 0027624429     PISSN: 10577149     EISSN: 19410042     Source Type: Journal    
DOI: 10.1109/83.236536     Document Type: Article

References (48)

1. H. Derin, H. Elliot, R. Cristi, and D. Geman, “Bayes smoothing algorithms for segmentation of binary images modeled by Markov random fields,” IEEE Trans. Patt. Anal. Mach. Intell., Vol. PAMI-6, pp. 707-720, Nov. 1984.
2. S. Geman and D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,” IEEE Trans. Trans. Patt. Anal. Mach. Intell., Vol. PAMI-6, pp. 721-741, Nov. 1984.
3. J. Besag, “On the statistical analysis of dirty pictures,” J. Roy. Statist. Soc. B, vol. 48, no. 3, pp. 259-302, 1986.
4. H. Derin and H. Elloit, “Modeling and segmentation of noisy and textured images using Gibbs random fields,” IEEE Trans. Patt. Anal. Mach. Intell., Vol. PAMI-9, pp. 39-55, Jan. 1987.
5. A. Blake and A. Zisserman, Visual Reconstruction. Cambridge, MA: MIT Press, 1987.
6. C. Bouman and B. Liu, “A multiple resolution approach to regularization,” in Proc. SPIE Conf. on Visual Comm. and Image Proc, Cambridge, MA, 1988, pp. 512-520.
7. S. Geman and D. McClure, “Bayesian image analysis: an application to singel photon emission tomography,” in Proc. Statist. Comput. Sect. Amer. Stat. Assoc, Washington, DC, 1985, pp. 12-18.
8. S. Geman and D. McClure, “Statistical methods for tomographic image reconstruction,” Bull. Int. Stat. Inst., vol. LII-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. Im., Vol. 8, pp. 194-202, June 1989.
10. R. Stevenson and E. Delp, “Fitting Curves with Discontinuities,” in Proc. of the 1st Int. Wkshp. on Robust Comput. Vision, Seattle, WA, 1990, pp. 127-136.
11. P. Huber, Robust Statistics. New York: John Wiley & Sons, 1981.
12. P. J. Green, “Bayesian reconstructions from emission tomogrpahy data using a modified EM algorithm, IEEE Trans. Med. Im., Vol. 9, pp. 84-93, Mar. 1990.
13. K. Lange, “Convergence of EM image reconstruction algorithms with Gibbs priors,” IEEE Trans. Med. Im., Vol. 9, pp. 439-446, Dec. 1990.
14. S. A. Kassam, Signal Detection in Non-Gaussian Noise. New York: Springer-Verlag, 1988.
15. G. T. Herman, H. Hurwitz, A. Lent, and H-P. Lung, “On the Bayesian approach to image reconstruction,” Info, and Cont., vol. 42, pp. 60–71, 1979.
16. K. M. Hanson and G. W. Wecksung, “Bayesian approach to limited-angle reconstruction in computed tomography,” J. Opt. Soc. Am., Vol. 73, No. 11, pp. 1501-1509, Nov. 1983.
17. 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.
18. J. Marroquin, S. Mitter, and T. Poggio, “Probabilistic solution of ill-posed problems in computational vision,” J. of the Am. Stat. Assoc, Vol. 82, pp. 76-89, Mar. 1987.
19. B. Horn and B. Schunck, “Determining optical flow,” Artifical Intelligence, vol. 17, pp. 185–203, 1981.
20. K. Ikeuchi and B. Horn, “Numerical shape from shading and occluding boundaries,” Artificial Intelligence, vol. 17, pp. 141–183, 1981.
21. V. Torre and T. Poggio, “On edge detection,” IEEE Trans. Patt. Anal. Mach. Intell, Vol. PAMI-8, pp. 147-163, Mar. 1986.
22. H. Van Trees, Detection, Estimation, and Modulation Theory. New York: John Wiley & Sons, 1968.
23. C. Bouman and B. Liu, “Multiple resolution segmentation of textured images,” IEEE Trans. Patt. Anal. Mach. Intell, Vol. 13, pp. 99-113, Feb. 1990.
24. J. Besag, “Spatial interaction and the statistical analysis of lattice systems,” J. Royal Stat. Soc. B, vol. 36, pp. 192–326, 1974.
25. R. Kinderman and J. L. Snell, Markov Random Fields and their Applications. Providence: American Mathematical Society, 1980.
26. J. Hutchinson, C. Koch, J. Luo, and C. Mead, “Computing motion using analog and binary resistive networks,” Computer, Vol. 21, pp. 53-63, Mar. 1988.
27. D. Geman and G. Reynolds, “Constrained restoration and the recovery of discontinuities,” IEEE Trans. Patt. Anal. Mach. Intell., Vol. 14, pp. 367-383, Mar. 1992.
28. C. Bouman and K. Sauer, “An edge preserving method for image reconstruction from integral projections,” in Proc. Conf. on Inf. Sei. and Sys., Johns Hopkins University, Baltimore, MD, 1991, pp. 382-387.
29. N. Gallagher and G. Wise, “A theoretical analysis of the properties of median filters,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-29, pp. 1136-1141, Dec. 1981.
30. E. J. Coyle and J. H. Lin, “Stack filters and the mean absolute error criterion,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. 36, pp. 1244-1254, Aug. 1988.
31. A. Tikhonov and V. Arsenin, Solutions of Ill-Posed Problems. New York: Winston and Sons, 1977.
32. C. Bouman and K. Sauer, “A generalized Gaussian image model for edge-preserving MAP estimation,” School of Elect. Eng., Purdue Univ., Tech. Rep. TR-EE-92-1, Jan. 1992.
33. J. Zhang and J. W. Modestino, “A model-fitting approach to cluster validation with application to stochastic model-based image segmentation,” in Proc. IEEE Int. Conf. on Acoust., Speech, Signal Proc, New York, NY, 1988, pp. 1148-1151.
34. J. Besag, “Towards Bayesian image analysis,” J. Applied Stat., vol. 16, no. 3, pp. 395-407, 1989.
35. W. Rey, Introduction to Robust and Quasi-Robust Statistical Methods. Berlin: Springer-Verlag, 1980.
36. T. Nodes and N. Gallagher, “Median filters: some modifications and their properties,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-30, pp. 739-746, Oct. 1982.
37. J. P. Fitch, E. Coyle, and N. Gallagher, “Root Properties and Convergence Rates of Median Filters,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-33, pp. 230-239, Feb. 1985.
38. F. Beckman, “The solution of linear equations by the conjugate gradient method,” in Mathematical Methods for Digital Computers, A. Ralston, H. Wilf, and K. Enslein, Eds. New York: Wiley, 1960.
39. O. Yli-Harja, J. Astola, and Y. Neuvo, “Analysis of the properties of median and weighted median filters using threshold logic and stack filter representation,” IEEE Trans. Signal Processing, Vol. 39, Feb. 1991.
40. J. Astola and Y. Neuvo, “Matched median filtering,” to be published in IEEE Trans. Commun.
41. K. Sauer and C. Bouman, “Bayesian estimation of transmission tomograms using segmentation based optimization,” IEEE Trans. Nuclear Science, Vol. 39, pp. 1144-1152, Aug. 1992.
42. K. Sauer and C. Bouman, “Bayesian estimation from projections with low photon dosages,” in Proc. of IEEE Int. Conf. on Acoust, Speech and Signal Proc, Toronto, Canada, 1991, pp. 2593-2596.
43. K. Sauer and C. Bouman, “A local update strategey for iterative reconstruction from projections,” IEEE Trans. Signal Processing, vo. 41, pp. 534–548, Feb. 1993.
44. C. Bouman and K. Sauer, “Nonlinear multigrid methods of optimization in Bayesian tomographic image reconstruction,” to appear in the Proc. of SPIE Conf. on Neural and Stochastic Methods in Image and Signal Processing, San Diego, CA, 1992, pp. 296-306.
45. R. DeVore and B. Lucier, “Fast wavelet techniques for near-optimal image processing,” in Proc. of IEEE Military Communications Conference, San Diego, CA, 1992, pp. 1129-1135.
46. P. Meer, D. Mintz, and A. Rosenfeld, “Robust regression methods for computer vision: a review,” Inter. J. of Comp. Vision, Vol. 6, No. 1, pp. 59-70, Apr. 1983.
47. D. M. Young, Iterative Solution of Large Linear Systems. New York: Academic Press, 1971.
48. S. P. Boyd and C. H. Barrett, Linear Controller Design-Limits of Performance. Englewood Cliffs, NJ: Prentice-Hall, 1991.