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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\n            <jats:italic>L<\/jats:italic>\n            <jats:sup>2<\/jats:sup>\n            distances of the denoised version to the original image.\n          <\/jats:p>","DOI":"10.1145\/1941487.1941513","type":"journal-article","created":{"date-parts":[[2011,4,26]],"date-time":"2011-04-26T12:01:31Z","timestamp":1303819291000},"page":"109-117","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":32,"title":["Self-similarity-based image denoising"],"prefix":"10.1145","volume":"54","author":[{"given":"Antoni","family":"Buades","sequence":"first","affiliation":[{"name":"Universit\u00e9 Paris Descartes, Paris, France"}]},{"given":"Bartomeu","family":"Coll","sequence":"additional","affiliation":[{"name":"Universitat Illes Balears, Palma de Mallorca, Spain"}]},{"given":"Jean-Michel","family":"Morel","sequence":"additional","affiliation":[{"name":"CMLA, ENS Cachan, France"}]}],"member":"320","published-online":{"date-parts":[[2011,5]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531327"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/0729052"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-03641-5_26"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1037\/h0054663"},{"key":"e_1_2_1_5_1","volume-title":"5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2008 (Paris, France, May 14--17, 2008), ISBI 2008, 748--751","author":"Boulanger J.","unstructured":"Boulanger , J. , Sibarita , J. , Kervrann , C. , Bouthemy , P. Non-parametric regression for patch-based fluorescence microscopy image sequence denoising . In 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2008 (Paris, France, May 14--17, 2008), ISBI 2008, 748--751 . Boulanger, J., Sibarita, J., Kervrann, C., Bouthemy, P. Non-parametric regression for patch-based fluorescence microscopy image sequence denoising. In 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2008 (Paris, France, May 14--17, 2008), ISBI 2008, 748--751."},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/040616024"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-006-0029-y"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2006.871137"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-007-0052-1"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2009.2017171"},{"key":"e_1_2_1_11_1","volume-title":"SPIE7246","author":"Chatterjee P.","year":"2009","unstructured":"Chatterjee , P. , Milanfar , P. Image denoising using locally learned dictionaries. Comput. Imag. VII , SPIE7246 ( 2009 ), 72460V--72460V. Chatterjee, P., Milanfar, P. Image denoising using locally learned dictionaries. Comput. Imag. 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