Unsupervised edge-preserving image restoration via a saddle point approximation

Image and Vision Computing

Volumn 17, Issue 11, 1999, Pages 779-793

  Bedini, Luigi ^a   Tonazzini, Anna ^a   Minutoli, Salvatore ^a  

^a ISTI CNR   (Italy)

Author keywords

Edge preserving regularization; Gibbs parameter estimation; Unsupervised image restoration

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; MARKOV PROCESSES; MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD ESTIMATION; PARAMETER ESTIMATION;

EDGE PRESERVING REGULARIZATION; GIBBS PARAMETER ESTIMATION; UNSUPERVISED IMAGE RESTORATION;

IMAGE RECONSTRUCTION;

EID: 0033359282     PISSN: 02628856     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0262-8856(98)00154-1     Document Type: Article

References (43)

1. S. Geman, D. Geman, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Trans. Patt. Anal. Mach. Intell. 6 (1984) 721-740.
2. J. Marroquin, S. Mitter, T. Poggio, Probabilistic solution of ill-posed problems in computational vision, J. Am. Stat. Ass. 82 (1987) 76-89.
3. S. Kirkpatrick, C.D. Gellatt, M.P. Vecchi, Optimisation by simulated annealing, Science 220 (1983) 671-680.
4. A. Blake, A. Zisserman, Visual Reconstruction, MIT Press, Cambridge, USA, 1987.
5. D. Geiger, F. Girosi, Parallel and deterministic algorithms for MRFs: surface reconstruction, IEEE Trans. Patt. Anal. Mach. Intell. 13 (1991) 401-412.
6. G.L. Bilbro, W.E. Snyder, Applying mean field annealing to image noise removal, J. Neural Network Comput. Fall, (1990) 5-17.
7. J. Besag, On the statistical analysis of dirty pictures, J. R. Statist. Soc. ser. B 48 (1986) 259-302.
8. A.P. Dempster, N.M. Laird, D.B. Rubin, Maximum Likelihood from incomplete data via the EM algorithm, J. R. Statist. Soc. ser. B 39 (1977) 1-38.
9. T. Hebert, R. Leahy, A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors, IEEE Trans. Med. Imag. 8 (1989) 194-202.
10. L. Bedini, E. Salerno, A. Tonazzini, Edge-preserving tomographic reconstruction from Gaussian data using a Gibbs prior and a generalized Expectation-Maximization algorithm, Int. J. Imag. Systems Technol. 5 (1994) 231-238.
11. G. Winkler, Image analysis, random fields and dynamic Monte Carlo methods: a mathematical introduction, Springer-Verlag, Berlin, 1995.
12. B. Gidas, Parameter estimation for Gibbs distributions from fully observed data, in: R. Chellappa and A. Jain (Eds.), Markov Random Fields Theory and Application, Academic Press, San Diego, 1993, pp. 471-498.
13. L. Younes, Estimation and annealing for Gibbsian fields, Ann. Inst. Henri Poincare 24 (2) (1988) 269-294.
14. S.Z. Li, Markov Random Field Modeling in Computer Vision, Springer, Tokyo, 1995.
15. G.R. Cross, A.K. Jain, Markov random field texture models, IEEE Trans. Patt. Anal. Mach. Intell. 5 (1983) 25-39.
16. H. Derin, S. Guler, Realizations and parameter estimation for line processes, Proc. Int. Conf Acoust. Speech Signal. Process. 90 IV (1990) 2213-2216.
17. L. Bedini, X. Qiao, A. Tonazzini, A generalized Boltzmann machine for learning Gibbs priors in edge-preserving image restoration, IEI Technical Report B4-55, 1995.
18. R. Azencott, Synchronous Boltzmann machines and Gibbs fields: learning algorithms, in: F. Fogelman and J. Hérault (Eds.), Neuro-computing, NATO ASI F 68, 1990, pp. 51-64.
19. R. Azencott, Boltzmann machines: high-order interactions and synchronous learning, in: P. Barone and A. Frigessi (Eds.), Stochastic models in image analysis, Lecture Notes in Statistics, Springer-Verlag, 1992, pp. 14-45.
20. G.E. Hinton, T.J. Sejnowski, D.H. Hackley, Boltzmann machine: constraint satisfaction networks that learn, Carnegie-Mellon University Technical Report CNU-CS-84-119, 1984.
21. E. Aarts, J. Korst, Simulated Annealing and Boltzmann Machines, Wiley, 1989.
22. L. Bedini, S. Pandolfi, A. Tonazzini, Training a Boltzmann machine for edge-preserving image restoration, SPIE's 1993 International Symposium on Optical Instrumentation and Applied Sciences, Proc, Proc. Neural Stochastic Meth. Image Signal Process. II 2032 (1993) 192-202.
23. M. Bertero, T. Poggio, V. Torre, I11-posed problems in early vision, Proc. IEEE 76 (8) (1988) 869-889.
24. D. Geman, G. Reynolds, Constrained restoration and the recovery of discontinuities, IEEE Trans. Patt. Anal. Mach. Intell. 14 (1992) 367-383.
25. G. Wahba, Practical approximate Solutions to Linear Operator Equations when the Data Are Noisy, SIAM J. Numer. Anal. 14, 1977.
26. P. Hall, D.M. Titterington, Common structure of techniques for choosing smoothing parameters in regression problems, J. R. Stat. Soc. B 49 (1987) 184-198.
27. G.H. Golub, M. Heath, G. Wahba, Generalized cross-validation as a method for choosing a good ridge parameter, Technometrics 21 (1979) 215-223.
28. S. Geman, D.E. McClure, Statistical methods for tomographic image reconstruction, Proc. of the 46th session of the ISI, Bull. ISI 52 (1987) 1-18.
29. S. Lakshmanan, H. Derin, Simultaneous parameter estimation and segmentation of Gibbs random fields using simulated annealing, IEEE Trans. Patt. Anal. Mach. Intell. 11 (1989) 799-813.
30. J. Zhang, The mean field theory in EM procedures for Markov random fields, IEEE Trans, on Signal. Process. 40 (10) (1992) 2570-2583.
31. J. Zhang, The mean field theory in EM procedures for blind Markov random field image restoration, IEEE Trans. Image Process. 2 (1) (1993) 27-40.
32. C.J. Geyer, E.A. Thompson, Constrained Monte Carlo maximum likelihood for dependent data, J. R. Statist. Soc. ser. B 54 (1992) 657-699.
33. D.M. Higdon, V.E. Johnson, T.G. Turkington, J.E. Bowsher, D.R. Gilland, R.J. Jaszczak, Fully Bayesian estimation of Gibbs hyperparameters for emission computed tomography data, Technical Report 96-21, Institute of Statistics and Decision Sciences, Duke University, 1995.
34. X. Escombes, R. Morris, J. Zerubia, M. Berthod, Maximum likelihood estimation of Markov random field parameters using Markov chain Monte Carlo algorithms, in: M. Pelillo and E.R Hancock (Eds.), Lecture Notes in Computer Science 1223, 1997, pp. 133-148.
35. A. Tonazzini, L. Bedini, S. Minutoli, Joint MAP image restoration and ML parameter estimation using MRF models with explicit lines, IASTED Int. Conf. on Signal and Image Processing (SIP'97), New Orleans, 1997.
36. H. C. Andres, B. R. Hunt, Digital Image Restoration, Prentice-Hall, Englewood Cliffs, NJ, USA, 1977.
37. L. Bedini, I. Gerace, E. Salerno, A. Tonazzini, Models and algorithms for edge-preserving image reconstruction, in: P.W. Hawkes (Ed.), Adv. Imag. Electron Phys., vol. 97, 1996, pp. 86-189.
38. L. Bedini, I. Gerace, A. Tonazzini, A deterministic algorithm for reconstructing images with interacting discontinuities, CVGIP: Graphic. Models Image Process. 56 (2) (1994) 109-123.
39. J.L. Marroquin, Probabilistic solution of inverse problems, MIT-AI Technical Report 860, 1985.
40. L. Bedini, A. Tonazzini, Image restoration preserving discontinuities: the Bayesian approach and neural networks, Image Vision Comput. 10 (1992) 108-118.
41. J.J. Hopfield, Neurons with graded response have collective computa-tional properties like those of two-state neurons, Proc. Natl Acad. Sci. USA 81 (1984) 3088-3092.
42. D. Chandler, Introduction to modern statistical mechanics, Oxford University Press, 1987.
43. L. Bedini, I. Gerace, A. Tonazzini, A GNC algorithm for constrained image reconstruction with continuous-valued line processes, Pattern Recog. Lett. 15 (9) (1994) 907-918.