Anisotropic nonlocal means denoising

Arian Maleki; Manjari Narayan; Richard G. Baraniuk

doi:10.1016/j.acha.2012.11.003

Anisotropic nonlocal means denoising

Arian Maleki, Manjari Narayan, Richard G. Baraniuk

Houston Methodist

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

34 Scopus citations

Abstract

It has recently been proved that the popular nonlocal means (NLM) denoising algorithm does not optimally denoise images with sharp edges. Its weakness lies in the isotropic nature of the neighborhoods it uses to set its smoothing weights. In response, in this paper we introduce several theoretical and practical anisotropic nonlocal means (ANLM) algorithms and prove that they are near minimax optimal for edge-dominated images from the Horizon class. On real-world test images, an ANLM algorithm that adapts to the underlying image gradients outperforms NLM by a significant margin.

Original language	English (US)
Pages (from-to)	452-482
Number of pages	31
Journal	Applied and Computational Harmonic Analysis
Volume	35
Issue number	3
DOIs	https://doi.org/10.1016/j.acha.2012.11.003
State	Published - Nov 2013

Keywords

Anisotropy
Denoising
Minimax risk
Nonlocal means

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.acha.2012.11.003

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title = "Anisotropic nonlocal means denoising",

abstract = "It has recently been proved that the popular nonlocal means (NLM) denoising algorithm does not optimally denoise images with sharp edges. Its weakness lies in the isotropic nature of the neighborhoods it uses to set its smoothing weights. In response, in this paper we introduce several theoretical and practical anisotropic nonlocal means (ANLM) algorithms and prove that they are near minimax optimal for edge-dominated images from the Horizon class. On real-world test images, an ANLM algorithm that adapts to the underlying image gradients outperforms NLM by a significant margin.",

keywords = "Anisotropy, Denoising, Minimax risk, Nonlocal means",

author = "Arian Maleki and Manjari Narayan and Baraniuk, {Richard G.}",

note = "Funding Information: This work was supported by the grants NSF CCF-0431150, CCF-0926127, and CCF-1117939; DARPA/ONR N66001-11-C-4092 and N66001-11-1-4090; ONR N00014-08-1-1112, N00014-10-1-0989, and N00014-11-1-0714; AFOSR FA9550-09-1-0432; ARO MURI W911NF-07-1-0185 and W911NF-09-1-0383; and the TI Leadership University Program.",

year = "2013",

month = nov,

doi = "10.1016/j.acha.2012.11.003",

language = "English (US)",

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pages = "452--482",

journal = "Applied and Computational Harmonic Analysis",

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T1 - Anisotropic nonlocal means denoising

AU - Maleki, Arian

AU - Narayan, Manjari

AU - Baraniuk, Richard G.

N1 - Funding Information: This work was supported by the grants NSF CCF-0431150, CCF-0926127, and CCF-1117939; DARPA/ONR N66001-11-C-4092 and N66001-11-1-4090; ONR N00014-08-1-1112, N00014-10-1-0989, and N00014-11-1-0714; AFOSR FA9550-09-1-0432; ARO MURI W911NF-07-1-0185 and W911NF-09-1-0383; and the TI Leadership University Program.

PY - 2013/11

Y1 - 2013/11

N2 - It has recently been proved that the popular nonlocal means (NLM) denoising algorithm does not optimally denoise images with sharp edges. Its weakness lies in the isotropic nature of the neighborhoods it uses to set its smoothing weights. In response, in this paper we introduce several theoretical and practical anisotropic nonlocal means (ANLM) algorithms and prove that they are near minimax optimal for edge-dominated images from the Horizon class. On real-world test images, an ANLM algorithm that adapts to the underlying image gradients outperforms NLM by a significant margin.

AB - It has recently been proved that the popular nonlocal means (NLM) denoising algorithm does not optimally denoise images with sharp edges. Its weakness lies in the isotropic nature of the neighborhoods it uses to set its smoothing weights. In response, in this paper we introduce several theoretical and practical anisotropic nonlocal means (ANLM) algorithms and prove that they are near minimax optimal for edge-dominated images from the Horizon class. On real-world test images, an ANLM algorithm that adapts to the underlying image gradients outperforms NLM by a significant margin.

KW - Anisotropy

KW - Denoising

KW - Minimax risk

KW - Nonlocal means

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DO - 10.1016/j.acha.2012.11.003

M3 - Article

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EP - 482

JO - Applied and Computational Harmonic Analysis

JF - Applied and Computational Harmonic Analysis

IS - 3

ER -

Anisotropic nonlocal means denoising

Abstract

Keywords

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