Diffusion Interpretation of Nonlocal Neighborhood Filters for Signal Denoising | Zendy

Amit Singer | Zendy; Yoel Shkolnisky | Zendy; Boaz Nadler | Zendy

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Diffusion Interpretation of Nonlocal Neighborhood Filters for Signal Denoising

Author(s) -

Amit Singer,

Yoel Shkolnisky,

Boaz Nadler

Publication year - 2009

Publication title -

siam journal on imaging sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.944

H-Index - 71

ISSN - 1936-4954

DOI - 10.1137/070712146

Subject(s) - noise reduction , probabilistic logic , interpretation (philosophy) , diffusion , signal (programming language) , random walk , mathematics , algorithm , image denoising , decomposition , operator (biology) , computer science , diffusion map , space (punctuation) , signal processing , artificial intelligence , pattern recognition (psychology) , dimensionality reduction , statistics , physics , nonlinear dimensionality reduction , digital signal processing , repressor , ecology , chemistry , biology , biochemistry , transcription factor , thermodynamics , programming language , gene , operating system , computer hardware

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.

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