@article{fc7b29dbc8ce4a0ca880bcc2c46fd40f,
title = "Diffusion interpretation of nonlocal neighborhood filters for signal denoising",
abstract = "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.",
keywords = "Denoising, First passage time, Fokker-planck equation, Neighborhood filters, Nonlocal means",
author = "Amit Singer and Yoel Shkolnisky and Boaz Nadler",
note = "Funding Information: ∗Received by the editors January 2, 2008; accepted for publication (in revised form) October 20, 2008; published electronically January 30, 2009. The work of the first and second authors was supported in part by DARPA DSO (Dr. Cindy Daniell PM) under AFOSR contract FA9550-07-C-0024 (Dr. Fariba Fahroo PM). http://www.siam.org/journals/siims/2-1/71214.html †Department of Mathematics and PACM, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000 (amits@math.princeton.edu). The first author{\textquoteright}s research was supported by the Yale University-Weizmann Institute Joint Research Fund. ‡Department of Mathematics, Program in Applied Mathematics, Yale University, 10 Hillhouse Ave., P.O. Box 208283, New Haven, CT 06520-8283 (yoel.shkolnisky@yale.edu). §Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel (boaz.nadler@weizmann.ac.il). This author{\textquoteright}s research was supported by the Israeli Science Foundation (grant 432/06) and by the Lord Sieff of Brimpton memorial fund.",
year = "2009",
doi = "10.1137/070712146",
language = "English (US)",
volume = "2",
pages = "118--139",
journal = "SIAM Journal on Imaging Sciences",
issn = "1936-4954",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",
}