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

概率信息处理的专题审查，包括建模和近似算法的基本原理的物理力学技术的手段发表在物理学杂志A，第1.35卷，第37期。本文从平均场近似和Bethe近似两个方面阐述了概率图像处理算法的基本理论。对基于严格不等式的概率系统统计性能的分析方法进行了评述。2002年该刊的专题综述被评为该刊网页下载量二等奖。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Gaussian图模型的置信传播算法。该算法包括从观测数据的概率模型的统计学习。最大似然估计是统计学中的一种基本方法，它的统计学习是通过最大似然估计实现的。结果发表在Journal of Physics A，vol.36，no.43和vol.37，no.36上。特别值得一提的是，我们的论文受到了高度评价，其中一张照片被作为该杂志第36期第1.37卷的封面图片。该算法已被推广到广义的信念传播。部分结果已发表在IEICE Transactions on Information and Systems（D-II），vol.J88-D-II，no.12。在一些数值实验中，它已被证实，我们提出的算法可以给我们的高性能在合理的计算时间在个人计算机上，我们已经成功地构建了理论的自适应图像处理滤波器的基础上的马尔可夫随机场模型。

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.