Variational Bayesian image restoration based on a product of t-distributions image prior

IEEE Transactions on Image Processing

Volumn 17, Issue 10, 2008, Pages 1795-1805

  Chantas, Giannis ^a   Galatsanos, Nikolaos ^b   Likas, Aristidis ^a   Saunders, Michael ^c  

^a UNIVERSITY OF IOANNINA   (Greece)

^b UNIVERSITY OF PATRAS   (Greece)

^c STANFORD UNIVERSITY   (United States)

Author keywords

Constrained variational inference; Image restoration; Product prior; Student's t prior; Variational Bayesian inference

Indexed keywords

COLLEGE BUILDINGS; IMAGE RECONSTRUCTION; INFERENCE ENGINES; KETONES; REPAIR; RESTORATION;

BAYESIAN ALGORITHMS; BAYESIAN INFERENCES; CLOSED FORM; CONSTRAINED VARIATIONAL INFERENCE; IMAGE RESTORATION; IMAGE RESTORATION PROBLEM; MULTIPLE CONSTRAINTS; NUMERICAL EXPERIMENTS; PRODUCT PRIOR; STUDENT'S-T PRIOR; T-DISTRIBUTIONS; VARIATIONAL BAYESIAN; VARIATIONAL BAYESIAN INFERENCE;

BAYESIAN NETWORKS;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; BAYES THEOREM; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE SUBTRACTION; METHODOLOGY; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; STATISTICAL MODEL;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; BAYES THEOREM; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; MODELS, STATISTICAL; PATTERN RECOGNITION, AUTOMATED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SUBTRACTION TECHNIQUE;

EID: 52649142740     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2008.2002828     Document Type: Article

References (33)

1. G. Demoment, "Image reconstruction and restoration: Overview of common estimation structures and problems," IEEE Trans. Signal Process., vol. 37, no. 12, pp. 2024-2036, Dec. 1989.
2. N. P. Galatsanos and A. K. Katsaggelos, "Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation," IEEE Trans. Image Process., vol. 1, no. 3, pp. 322-336, Jul. 1992.
3. R. Molina, A. K. Katsaggelos, and J. Mateos, "Bayesian and regularization methods for hyper-parameter estimation in image restoration," IEEE Trans. Image Process., vol. 8, no. 2, pp. 231-246, Feb. 1999.
4. C. Bouman and K. Sauer, "A generalized Gaussian image model for edge preserving MAP estimation," IEEE Trans. Image Process., vol. 2, no. 3, pp. 296-310, Jul. 1993.
5. R. R. Schultz and R. L. Stevenson, "A Bayesian approach to image expansion with improved resolution," IEEE Trans. Image Process., vol. 3, no. 5, pp. 233-242, May 1994.
6. R. Pan and S. Reeves, "Efficient Huberov edge preserving image restoration," IEEE Trans. Image Process., vol. 15, no. 12, pp. 3728-3735, Dec. 2006.
7. J. Portilla, V. Strella, M. Wainwright, and E. Simoncelli, "Image denoising using scale mixtures of Gaussians in the wavelet domain," IEEE Trans. Image Process., vol. 12, no. 11, pp. 1338-1351, Nov. 2003.
8. T. F. Chan, S. Esedoglu, F. Park, and M. H. Yip, "Recent developments in total variation image restoration," in Handbook of Mathematical Models in Computer Vision. New York: Springer, 2005.
9. J. Bioucas-Dias, M. Figueiredo, and J. Oliveira, "Adaptive Bayesian/ total-variation image deconvolution: A majorization-minimization approach," presented at the Eur. Signal Processing Conf. - EUSIPCO, Florence, Italy, Sep. 2006.
10. J. Bioucas-Dias, M. Figueiredo, and J. Oliveira, "Total-variation image deconvolution: A majorization-minimization approach," presented at the Int. Conf. Acoustics and Speech and Signal Processing, ICASSP, May 2006.
11. S. D. Babacan, R. Molina, and A. K. Katsaggelos, "Parameter estimation in TV image restoration using variational distribution approximation," IEEE Trans. Image Process., vol. 17, no. 3, pp. 326-339, Mar. 2008.
12. M.A.T. Figueiredo and R. D. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Trans. Image Process., vol. 12, no. 8, pp. 866-881, Aug. 2003.
13. J. M. Bioucas-Dias, "Bayesian wavelet-based image deconvolution: A GEM algorithm exploiting a class of heavy-tailed priors," IEEE Trans. Image Process., vol. 15, no. 4, pp. 937-951, Apr. 2006.
14. K. Hirakawa and X.-L. Meng, "An empirical bayes EM-wavelet unification for simultaneous denoising, interpolation, and/or demosaicing," presented at the IEEE Int. Conf. Image Processing, Atlanta, GA, Sep. 2006.
15. S. Roth and M. J. Black, "Fields of experts: A framework for learning image priors," in Proc. IEEE Conf. Computer Vision and Pattern Recognition, Jun. 2005, vol. II, pp. 860-867.
16. D. Sun and W.-K. Cham, "Postprocessing of low bit-rate block DCT coded images based on a fields of experts prior," IEEE Trans. Image Process., vol. 16, no. 11, pp. 2743-2751, Nov. 2007.
17. G. Chantas, N. P. Galatsanos, and A. Likas, "Bayesian restoration using a new nonstationary edge-preserving image prior," IEEE Trans. Image Process., vol. 15, no. 10, pp. 2987-2997, Oct. 2006.
18. G. K. Chantas, N. P. Galatsanos, and N. Woods, "A super-resolution based on fast registration and maximum a posteriori reconstruction," IEEE Trans. Image Process., vol. 16, no. 7, pp. 1821-1830, Jul. 2007.
19. D. Tzikas, A. Likas, and N. Galatsanos, "Variational Bayesian blind image deconvolution with student-t priors," presented at the IEEE Int. Conf. Image Processing, San Antonio, TX, Sep. 2007.
20. A. Kanemura, S.-I. Maeda, and S. Ishii, "Hyperparameter estimation in Bayesian image superresolution with a compound Markov random field prior," in Proc. IEEE Int. Workshop on Machine Learning for Signal Processing, Thessaloniki, Greece, Aug. 2007, pp. 181-186.
21. A. Mairgiotis, N. Galatsanos, and Y. Yang, "New detectors for watermarks with unknown power based on student-t image priors," presented at the IEEE Int. Conf. Multimedia Signal Processing, MMSP, Chania, Crete, 2007.
22. C. Bishop, Pattern Recognition and Machine Learning. New York: Springer Verlag, 2006.
23. M. E. Tipping, "Sparse Bayesian learning and the relevance vector machine," J. Mach. Learn. Res., vol. 1, pp. 211-244, 2001.
24. C. Nikias and M. Shao, Signal Processing with Alpha-Stable Distributions and Applications.. New York: Wiley, 1995.
25. M.N. Do and M. Vetterli, "Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance," IEEE Trans. Image Process., vol. 11, no. 2, pp. 146-158, Feb. 2002.
26. A. L. Cunha, J. Zhou, and M. N. Do, "The nonsubsampled contourlet transform: Theory, design, and applications," IEEE Trans. Image Process., vol. 15, no. 10, pp. 3089-3101, Oct. 2006.
27. C. Liu and D. B. Rubin, "ML estimation of the t distribution using EM and its extensions," ECM and ECME, Statist. Sin., vol. 5, pp. 19-39, 1995.
28. A. Likas and N. Galatsanos, "A variational approach for Bayesian blind image deconvolution," IEEE Trans. Signal Process., vol. 52, no. 8, pp. 2222-2233, Aug. 2004.
29. M. Beal, "Variational Algorithms for Approximate Bayesian Inference," Ph.D. Dissertation, The Gatsby Computational Neuroscience Unit, University College, London, U.K., 2003.
30. C. C. Paige and M. A. Saunders, "Solution of sparse indefinite systems of linear equations," SIAM J. Numer. Anal., vol. 12, pp. 617-629, 1975.
31. Y. Saad, Iterative Methods for Sparse Linear Systems, Second Edition Philadelphia, PA: SIAM, 2000.
32. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. Baltimore, MD: Johns Hopkins Univ. Press, 1996.
33. C.C. Paige and M. A. Saunders, "LSQR: An algorithm for sparse linear equations and sparse least squares," ACM Trans. Math. Softw., vol. 8, no. 1, pp. 43-71, 1982.