Diffusion Interpretation of Nonlocal Neighborhood Filters for Signal Denoising

被引：67

作者：

Singer, Amit ^{[1
,2
]}

Shkolnisky, Yoel ^{[3
]}

Nadler, Boaz ^{[4
]}

机构：

[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[2] Princeton Univ, PACM, Princeton, NJ 08544 USA

[3] Yale Univ, Dept Math, Program Appl Math, New Haven, CT 06520 USA

[4] Weizmann Inst Sci, Dept Comp Sci & Appl Math, IL-76100 Rehovot, Israel

来源：

SIAM JOURNAL ON IMAGING SCIENCES | 2009年 / 2卷 / 01期

关键词：

denoising; neighborhood filters; nonlocal means; Fokker-Planck equation; first passage time; NONLINEAR DIFFUSION; IMAGE; REGULARIZATION;

D O I：

10.1137/070712146

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Nonlocal neighborhood filters are modern and powerful techniques for image and signal denoising. In this paper, we give a probabilistic interpretation and analysis of the method viewed as a random walk on the patch space. We show that the method is intimately connected to the characteristics of diffusion processes, their escape times over potential barriers, and their spectral decomposition. In particular, the eigenstructure of the diffusion operator leads to novel insights on the performance and limitations of the denoising method, as well as a proposal for an improved filtering algorithm.

引用

页码：118 / 139

页数：22

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