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

基于统计力学技术的概率信息处理的专题综述，包括建模的基本原理和近似算法，发表在《物理学报》A卷1.35期，第37期。本文介绍了一些概率图像处理算法的基本原理，利用平均场和贝特近似解释了这些算法的基本原理。本文还评述了基于一些严格不等式的概率系统统计性能的分析方法。该专题评论在2002年该杂志网页的下载次数中排名第二。在2003年和2004年，本项目提出了一些将Bethe近似应用于Q-Ising模型和高斯图模型的信念传播算法。该算法包括从观测数据中对概率模型进行统计学习。利用最大似然估计实现了统计学习，最大似然估计是统计学的基础技术之一。研究结果以两篇论文的形式发表在《物理杂志A》第36卷第2期。第43卷和第37卷，第36期。特别值得注意的是，我们的论文得到了高度的赞赏，其中一张照片被采用为第1.37期的标题页的人物。杂志第36页。该算法已扩展到广义信念传播。部分研究结果已发表在IEICE信息和系统学报（D-II），第j88 -D-II卷，第12期。数值实验表明，本文提出的算法能够在合理的计算时间内获得较高的性能，并成功地构建了基于马尔可夫随机场模型的自适应图像处理滤波器理论。

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.