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We show that appropriate weights are required to avoid aliasing-like effects, and we provide an explicit convergence criterion for an associated dual minimization algorithm based on Chambolle's work. We study theoretical properties of the obtained local filter and show that this localization of the ROF model brings an interesting optimization of the bias-variance trade-off, and a strong reduction of an ROF drawback called the \u201cstaircasing effect.\u201d Finally, we present a new denoising algorithm, TV-means, that efficiently combines the idea of local TV-filtering with the nonlocal means patch-based method.<\/jats:p>","DOI":"10.1137\/100785855","type":"journal-article","created":{"date-parts":[[2011,6,21]],"date-time":"2011-06-21T18:51:21Z","timestamp":1308682281000},"page":"651-694","source":"Crossref","is-referenced-by-count":75,"title":["Total Variation as a Local Filter"],"prefix":"10.1137","volume":"4","author":[{"given":"C\u00e9cile","family":"Louchet","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lionel","family":"Moisan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,6,21]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-03-07004-7"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-007-9160-x"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/050634086"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.4171\/IFB\/112"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/s00208-004-0628-9"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/BF00375127"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.2001.3829"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"L. 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