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Statistical-mechanical analysis of dynamical properties of algorithms for image restoration

图像恢复算法动态特性的统计力学分析

基本信息

批准号：
14084201
负责人：
INOUE Jun-ichi
金额：
$ 5.06万
依托单位：
Hokkaido University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research on Priority Areas
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2005
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-14084201/
关键词：
Probabilistic image processing Statistical mechanics of information Bavesian Statistics EM algorithm Replica method Non-extensive statistical mechanics Quantum fluctuation Evaluation of statistical performance 統計力学情報科学画像修復ダイナミックス

项目摘要

In this research project, we investigated the dynamical properties of Bayesian image restoration for the blapk-while binary and gray-scaled images represented by the Ising and the Q-Ising models, respectively. We introduced the mean-field model to evaluate the accuracy or the speed of the convergence for EM algorithm and gradient descent method to obtain the maximum likelihood estimate for the hyper-parameters. We found that EM algorithm is superior to the gradient descent method in the speed of the convergence. Moreover, our analysis made it clear that the dynamical behavior of the hyper-parameters shows a kind of the "oscillating phenomena " before they converge to their true values if the time to wait until the system reaches to the equilibrium states is not enough.We also proposed a new-type of the deterministic annealing EM algorithm which was extended by means of non-extensive statistical mechanics. The method was applied to the problem of Traveling salesman and the statistical performance was investigated extensively.We also presented several applications of quantum spin glasses (random field Ising model, Shermgton-KJrkpatrick model, Ising spin glasses with p-body interaction in a transverse field) to probabilistic information processing, especially to the problems of image restoration and error-correcting codes. As a related optimization method, quantum annealing was also introduced to these research fields and its performance was investigated by using the quantum Markov chain Monte Carlo method. The Nishimori-Wong condition, on which the best possible performance of the quantum MPM estimation is achieved, was derived as a condition on the effective amplitude of the transverse field.

在本研究计划中，我们研究了贝叶斯图像恢复的动态特性的blapk-while二进制和灰度图像表示的伊辛和Q-Ising模型，分别。我们引入平均场模型来评价EM算法的收敛速度和精度，并引入梯度下降法来获得超参数的极大似然估计。我们发现EM算法在收敛速度上比梯度下降法有上级的优势。此外，我们的分析表明，当系统到达平衡态的时间不够长时，超参数的动力学行为在收敛到其真值之前表现出一种“振荡现象“，我们还提出了一种新的确定性退火EM算法，并利用非广延统计力学对该算法进行了推广。本文还介绍了量子自旋玻璃（随机场Ising模型、Shermgton-KJrkpatrick模型、横场中p体相互作用的Ising自旋玻璃）在概率信息处理，特别是图像恢复和纠错码问题中的应用。作为一种相关的优化方法，量子退火也被引入到这些研究领域，并使用量子马尔可夫链蒙特卡罗方法研究其性能。西森-王条件，量子MPM估计的最佳性能是实现，推导出作为条件的有效振幅的横向场。