Design of adaptive image processing filter based on Markov random field models

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The topical review of probabilistic information processing by means of statistical-mechanical techniques including the fundamentals of modeling and the approximate algorithms was published in the Journal of Physics A, Vo1.35, No.37. In the review, the fundamental theory of some probabilistic image processing algorithms was explained by using the mean-field and the Bethe approximations. The analytical methods for statistical performance of the probabilistic systems based on some rigorous inequalities were also reviewed. The topical review has been ranked as the second prize in the number of downloads from the webpage of the journal in 2002. In 2003 and 2004, some belief propagation algorithms by applying the Bethe approximation to Q-Ising model and Gaussian graphical model have been proposed by the present project. The algorithms include the statistical learning of the probabilistic models from observed data. The statistical learning has been achieved by employing the maximum likelihood estimation which is one of the preliminary techniques in the statistics. The results were published as two papers in the Journal of Physics A, vol.36, no.43 and vol.37, no.36. Particularly, our paper was highly appreciated and one of the photographs was adopted as a figure of the title page in vo1.37, no.36 of the journal. The algorithms have been extended to the generalized belief propagation. A part of the results has been published in the IEICE Transactions on Information and Systems (D-II), vol.J88-D-II, no.12. In some numerical experiments, it has been confirmed that the proposed algorithms can give us the high performance within the reasonable computational time in the personal computers and we have succeeded in constructing the theory of the adaptive image processing filters based on the Markov random field model.