Markovian reconstruction using a GNC approach

IEEE Transactions on Image Processing

Volumn 8, Issue 9, 1999, Pages 1204-1220

  Nikolova, Mila ^a  

^a UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

Continuation methods; Image reconstruction; Inverse problems; MAP estimation; Nonconvex optimization; Regularization

Indexed keywords

EID: 0013212015     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.784433     Document Type: Article

References (45)

1. J. E. Besag, "On the statistical analysis of dirty pictures (with discussion)," J. R. Stat. Soc. B, vol. 48, pp. 259-302, 1986.
2. _, "Digital image processing: Toward Bayesian image analysis," J. Appl. Stat., vol. 16, pp. 395-407, 1989.
3. G. Bilbro, W. Snyder, and R. Mann, "Mean-field approximation minimizes relative entropy," J. Opt. Soc. Amer., vol. 8, pp. 290-294, Feb. 1991.
4. G. Bilbro, W. Snyder, S. Garnier, and J. Gault, "Mean-field annealing: A formalism for constructing GNC-like algorithms," IEEE Trans. Neural Networks, vol. 3, pp. 131-138, Jan. 1992.
5. A. Blake and A. Zisserman, Visual Reconstruction. Cambridge, MA: MIT Press, 1987.
6. A. Blake, "Comparison of the efficiency of deterministic and stochastic algorithms for visual reconstruction," IEEE Trans. Pattern Anal. Machine Intell., vol. 11, pp. 2-12, Jan. 1989.
7. C. Bouman and B. Liu, "Segmentation of textured images using a multiple resolution approach," in Proc. IEEE ICASSP, Apr. 1988, pp. 1124-1127.
8. _, "A generalized Gaussian image model for edge-preserving MAP estimation," IEEE Trans. Image Processing, vol. 2, pp. 296-310, July 1993.
9. C. Bouman and K. Sauer, "A unified approach to statistical tomography using coordinate descent optimization," IEEE Trans. Image Processing, vol. 5, pp. 480-492, Mar. 1996.
10. P. Charbonnier, L. Blanc-Féraud, G. Aubert, and M. Barlaud, "Deterministic edge-preserving regularization in computed imaging," IEEE Trans. Image Processing, vol. 5, Dec. 1996.
11. n," SIAM J. Contr. Optim., vol. 25, p. 737, May 1987.
12. G. Demoment, "Image reconstruction and restoration: Overview of common estimation structure and problems," IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 2024-2036, Dec. 1989.
13. M. Duflo, Algorithmes Stochastiques, Collection Mathématiques et Applications 23. Berlin, Germany: Springer-Verlag, 1996.
14. D. Geiger and F. Girosi, "Parallel and deterministic algorithms from MRF's: Surface reconstruction," IEEE Trans. Pattern Anal. Machine Intell., vol. 13, pp. 401-412, May 1991.
15. M," SIAM J. Contr. Optim., vol. 29, pp. 999-1018, Sept. 1991.
16. M," SIAM J. Contr. Optim., vol. 31, pp. 111-131, Jan. 1993.
17. 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, Nov. 1984.
18. S. Geman and D. McClure, "Statistical methods for tomographic image reconstruction," Proc. 46th Session of the ISI, Bull. ISI, vol. 52, pp. 22-26, 1997.
19. D. Geman, Random Fields and Inverse Problems in Imaging: Lecture Notes in Mathematics. Berlin, Germany: Springer-Verlag, 1990.
20. D. Geman and G. Reynolds, "Constrained restoration and recovery of discontinuities," IEEE Trans. Pattern Anal. Machine Intell., vol. 14, pp. 367-383, Mar. 1992.
21. D. Geman and C. Yang, "Nonlinear image recovery with half-quadratic regularization," IEEE Trans. Image Processing, vol. 4, pp. 932-946, July 1995.
22. D. M. Grieg, B. T. Porteous, and A. H. Seheult, "Exact maximum a posteriori estimation for binary images," J. R. Stat. Soc. B, vol. 51, pp. 271-279, 1989.
23. G. Herman, Image Reconstruction from Projections. The Fundamentals of Computerized Tomography. New York: Academic, 1980.
24. P. J. Huber, Robust Statistics. New York: Wiley, 1981.
25. B. Hunt, "The application of constrained least squares estimation to image restoration by digital computer," IEEE Trans. Commun., vol. COMM-22, pp. 805-812, 1973.
26. F. Jeng and J. Woods, "Simulated annealing in compound Gaussian random fields," IEEE Trans. Inform. Theory, vol. 36, pp. 94-107, Jan. 1990.
27. A. Kak and M. Slaney, Principles of Computerized Tomographic Imaging. New York: IEEE Press, 1987.
28. L. Le Cam, "Maximum likelihood: An introduction," Int. Stat. Rev., vol. 58, pp. 153-171, 1990.
29. Y. Leclerc, "Constructing simple stable description for image partitioning," Int. J. Comput. Vis., vol. 3, pp. 73-102, 1989.
30. S. Z. Li, "On discontinuity-adaptive smoothness priors in computer vision," IEEE Trans. Pattern Anal. Machine Intell., vol. 17, pp. 576-586, June 1995.
31. J. Marroquin, "Deterministic interactive particle models for image processing and computer graphics," Comput. Vis., Graph., Image Process., vol. 55, pp. 408-417, 1993.
32. R. Molina, A. Katsaggelos, J. Mateos, and A. Hermoso, Restoration of Severely Blurred High Range Images Using Stochastic and Deterministic Relaxation Algorithms in Compound Gauss Markov Random Fields, in M. Pelilo, E. R. Hancock, Eds, Proc. EMMCVPR'97.
33. D. Mumford and J. Shah, "Boundary detection by minimizing functionals," in Proc. IEEE ICASSP, 1985, pp. 22-26.
34. M. Nikolova, "Non convex regularization and the recovery of edges," in Proc. IEEE Workshop on Nonlinear Signal and Image Processing, June 1995, pp. 1042-1045.
35. M. Nikolova, J. Idier, and A. Mohammad-Djafari, "Inversion of large-support ill-posed linear operators using a piecewise Gaussian MRF," IEEE Trans. Image Processing, vol. 8, pp. 571-585, Apr. 1999.
36. P. Perona and J. Malik, "Scale-space and edge detection using anisotropic diffusion," IEEE Trans. Pattern Anal. Machine Intell., vol. 12, pp. 629-639, July 1990.
37. W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C, the Art of Scientific Computing, 2nd ed.. Cambridge, U.K.: Cambridge Univ. Press, 1992.
38. N. Saito, "Superresolution of noisy band-limited data by data adaptive regularization and its application to seismic trace inversion," in Proc. IEEE ICASSP, Albuquerque, NM, Apr. 1990, pp. 1237-1240.
39. K. Sauer and C. Bouman, "A local update strategy for iterative reconstruction from projections," IEEE Trans. Signal Processing, vol. 41, pp. 534-548, Feb. 1993.
40. T. Simchony, R. Chellappa, and Z. Lichtenchtein, "Graduated nonconvexity algorithm for image estimation using compound Gauss Markov field models," in Proc. IEEE ICASSP, 1989, pp. 1417-1420.
41. W. Snyder et al., "Image relaxation: Restoration and feature extraction," IEEE Trans. Pattern Anal. Machine Intell., vol. 17, pp. 620-624, June 1995.
42. D. Terzopoulos, "Regularization of inverse visual problems involving discontinuities," IEEE Trans. Pattern Anal. Machine Intell., vol. 8, pp. 413-424, July 1986.
43. A. Tikhonov and V. Arsenin, Solutions of Ill-Posed Problems. Washington, DC: Winston, 1977.
44. E. Wasserstrom, "Numerical solutions by the continuation method," SIAM Rev., vol. 15, pp. 89-119, Jan. 1973.
45. C. Yang, "Efficient stochastic algorithms on locally bounded image space," Comput. Vis., Graph., Image Process.: Graph. Models Image Process., vol. 55, pp. 494-506, Nov. 1993.