Non-local euclidean medians

Kunal N. Chaudhury; Amit Singer

doi:10.1109/LSP.2012.2217329

Non-local euclidean medians

Kunal N. Chaudhury, Amit Singer

Research output: Contribution to journal › Article › peer-review

65 Scopus citations

Abstract

In this letter, we note that the denoising performance of Non-Local Means (NLM) can be improved at large noise levels by replacing the mean by the Euclidean median. We call this new denoising algorithm the Non-Local Euclidean Medians (NLEM). At the heart of NLEM is the observation that the median is more robust to outliers than the mean. In particular, we provide a simple geometric insight that explains why NLEM performs better than NLM in the vicinity of edges, particularly at large noise levels. NLEM can be efficiently implemented using iteratively reweighted least squares, and its computational complexity is comparable to that of NLM. We provide some preliminary results to study the proposed algorithm and to compare it with NLM.

Original language	English (US)
Article number	6295644
Pages (from-to)	745-748
Number of pages	4
Journal	IEEE Signal Processing Letters
Volume	19
Issue number	11
DOIs	https://doi.org/10.1109/LSP.2012.2217329
State	Published - 2012

All Science Journal Classification (ASJC) codes

Signal Processing
Applied Mathematics
Electrical and Electronic Engineering

Keywords

Euclidean median
Weiszfeld algorithm
image denoising
iteratively reweighted least squares (IRLS)
non-local means

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10.1109/LSP.2012.2217329

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title = "Non-local euclidean medians",

abstract = "In this letter, we note that the denoising performance of Non-Local Means (NLM) can be improved at large noise levels by replacing the mean by the Euclidean median. We call this new denoising algorithm the Non-Local Euclidean Medians (NLEM). At the heart of NLEM is the observation that the median is more robust to outliers than the mean. In particular, we provide a simple geometric insight that explains why NLEM performs better than NLM in the vicinity of edges, particularly at large noise levels. NLEM can be efficiently implemented using iteratively reweighted least squares, and its computational complexity is comparable to that of NLM. We provide some preliminary results to study the proposed algorithm and to compare it with NLM.",

keywords = "Euclidean median, Weiszfeld algorithm, image denoising, iteratively reweighted least squares (IRLS), non-local means",

author = "Chaudhury, {Kunal N.} and Amit Singer",

note = "Funding Information: Manuscript received July 11, 2012; revised August 29, 2012; accepted August 30, 2012. Date of publication September 07, 2012; date of current version September 11, 2012. The work of K. N. Chaudhury was supported in part by the Swiss National Science Foundation under Grant PBELP2-135867. The work of A. Singer was supported in part by the National Science Foundation under Award Award DMS-0914892, by the Air Force Office of Scientific Research under Award FA9550-09-1-0551, by the National Institute of General Medical Sciences under Award R01GM090200, and by the Alfred P. Sloan Foundation. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. H. Vicky Zhao.",

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N1 - Funding Information: Manuscript received July 11, 2012; revised August 29, 2012; accepted August 30, 2012. Date of publication September 07, 2012; date of current version September 11, 2012. The work of K. N. Chaudhury was supported in part by the Swiss National Science Foundation under Grant PBELP2-135867. The work of A. Singer was supported in part by the National Science Foundation under Award Award DMS-0914892, by the Air Force Office of Scientific Research under Award FA9550-09-1-0551, by the National Institute of General Medical Sciences under Award R01GM090200, and by the Alfred P. Sloan Foundation. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. H. Vicky Zhao.

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N2 - In this letter, we note that the denoising performance of Non-Local Means (NLM) can be improved at large noise levels by replacing the mean by the Euclidean median. We call this new denoising algorithm the Non-Local Euclidean Medians (NLEM). At the heart of NLEM is the observation that the median is more robust to outliers than the mean. In particular, we provide a simple geometric insight that explains why NLEM performs better than NLM in the vicinity of edges, particularly at large noise levels. NLEM can be efficiently implemented using iteratively reweighted least squares, and its computational complexity is comparable to that of NLM. We provide some preliminary results to study the proposed algorithm and to compare it with NLM.

AB - In this letter, we note that the denoising performance of Non-Local Means (NLM) can be improved at large noise levels by replacing the mean by the Euclidean median. We call this new denoising algorithm the Non-Local Euclidean Medians (NLEM). At the heart of NLEM is the observation that the median is more robust to outliers than the mean. In particular, we provide a simple geometric insight that explains why NLEM performs better than NLM in the vicinity of edges, particularly at large noise levels. NLEM can be efficiently implemented using iteratively reweighted least squares, and its computational complexity is comparable to that of NLM. We provide some preliminary results to study the proposed algorithm and to compare it with NLM.

KW - Euclidean median

KW - Weiszfeld algorithm

KW - image denoising

KW - iteratively reweighted least squares (IRLS)

KW - non-local means

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Non-local euclidean medians

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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