### Self-similarity-based image denoisingSelf-similarity-based image denoising

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 Author Buades, Antoni ♦ Coll, Bartomeu ♦ Morel, Jean-Michel Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Language English
 Abstract The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics. In spite of the sophistication of the recently proposed methods, most algorithms have not yet attained a desirable level of applicability. All show an outstanding performance when the image model corresponds to the algorithm assumptions but fail in general and create artifacts or remove image fine structures. The main focus of this paper is, first, to define a general mathematical and experimental methodology to compare and classify classical image denoising algorithms and, second, to describe the nonlocal means (NL-means) algorithm introduced in 2005 and its more recent extensions. The mathematical analysis is based on the analysis of the "method noise," defined as the difference between a digital image and its denoised version. NL-means, which uses image self-similarities, is proven to be asymptotically optimal under a generic statistical image model. The denoising performance of all considered methods are compared in four ways: mathematical, asymptotic order of magnitude of the method noise under regularity assumptions; perceptual-mathematical, the algorithms artifacts and their explanation as a violation of the image model; perceptual-mathematical, analysis of algorithms when applied to noise samples; quantitative experimental, by tables of $L^{2}$ distances of the denoised version to the original image. Description Affiliation: Université Paris Descartes, Paris, France (Buades, Antoni) || Universitat Illes Balears, Palma de Mallorca, Spain (Coll, Bartomeu) || CMLA, ENS Cachan, France (Morel, Jean-Michel) Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2005-08-01 Publisher Place New York Journal Communications of the ACM (CACM) Volume Number 54 Issue Number 5 Page Count 9 Starting Page 109 Ending Page 117

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Source: ACM Digital Library