Statistical analysis of the expectation-maximization algorithm with loopy belief propagation in Bayesian image modeling
Statistical analysis of the expectation-maximization algorithm with loopy belief propagation in Bayesian image modeling
复制标题
贝叶斯图像建模中循环置信传播期望最大化算法的统计分析
DOI：
10.1080/14786435.2011.624558
复制
发表时间：
2012
影响因子：
1.6
通讯作者：
D.M.Titterington
中科院分区：
文献类型：
--
作者：
Shun Kataoka;Muneki Yasuda;Kazuyuki Tanaka;D.M.Titterington
从统计-机械信息学的观点出发，针对贝叶斯图像建模，提出了一种新的基于期望最大化(EM)算法和循环信任传播(LBP)的超参数估计的统计方法。在本文中，我们给出了一种新的方案，用LBP算法计算EM算法中关于假设退化过程从给定原始图像产生的所有可能退化图像的轨迹的平均值。此外，我们还给出了一种新的方案，用于计算基于LBP的EM算法中关于假设先验概率分布生成的所有可能原始图像的轨迹的平均值。二值图像复原的贝叶斯图像模型被构造为正方形格子上具有随机外场和空间均匀近邻相互作用的伊辛模型。我们利用随机自旋系统的Bethe近似构造了计算LBP中某些统计量的上述随机平均值的方案。它们被归结为LBP中消息分布的联立积分方程组的解。给出了LBP算法的数值实验结果，并对基于LBP的EM二值图像复原算法的轨迹进行了统计分析。
New statistical approaches to hyperparameter estimation by means of the expectation-maximization (EM) algorithm and loopy belief propagation (LBP) are given for Bayesian image modeling from the standpoint of statistical-mechanical informatics. In the present paper, we give a new scheme for computing the average of the trajectory in the EM algorithm with LBP with respect to all the possible degraded images generated by the assumed degradation process from a given original image. Moreover, we also give a new scheme for computing the average of the trajectory in the EM algorithm with LBP with respect to all the possible original images generated by the assumed prior probability distribution. Bayesian image models for binary image restorations are constructed as Ising models with random external fields and spatially uniform nearest-neighbor interactions on the square lattice. Our schemes for computing the above random averages for some statistical quantities in LBP are constructed by means of the Bethe approximation for random spin systems. They are reduced to the solution of simultaneous integral equations for distributions of messages in LBP. We show the results of some numerical experiments in LBP as well as the statistical analysis of the trajectory in the EM algorithm for binary image restoration by LBP.