基于非局部泛函分析的图像处理  

Image Processing Based on Nonlocal Functional Analysis

作　　者：房少梅[1] 

机构地区：[1]华南农业大学数学系,广州广东510642

出　　处：《数学进展》2009年第6期649-656,共8页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.10576013;No.10871075);广东省自然科学基金(No.5300889).

摘　　要：高效图像除噪算法的探索,仍然是泛函分析、偏微分方程和统计学及其相关交叉领域的极具价值的挑战性课题.尽管近来给出了一些比较成熟的算法,然而大多数算法并没有达到实际应用中所期望的程度,尚有很大的改进余地.本文主要目的是:比较基于偏微分方程与泛函分析方法的图像处理的数学理论;在此基础上着重介绍近年国际上出现的与具有非局部性的邻域滤波紧密联系的非局部泛函分析的图像处理方法,并探讨与偏微分方程结合的可能性.The noise removal algorithm in image processing is one of the most significant and challenging tasks which lie in the wide field such as functional analysis,partial differential equation,statistics and some overlapping subjects related to image processing.Recently there develop some excellent algorithms,while most of them do not attain the levels which we expect in practice.Thus we need to make further efforts to improve the noise removal algorithm.The main purpose of our paper：firstly,we compare some mathematic theories of image processing based on partial differential equation and functional analysis methods;then we focus on introducing some nonlocal functional analysis methods of image processing which closely connected with neighborhood filters,and therefore discussing whether we can combined the nonlocal functional with partial differential equation.

关 键 词：非局部泛函分析 偏微分方程 图像处理 邻域滤波 

分 类 号：O175.29[理学—数学] TP391[理学—基础数学]