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As the constrained model is employed, we need only to input the noise level, and the estimation of the regularization parameter is not required in these imaging problems. Experimental results for such imaging problems are presented to illustrate the effectiveness of the proposed method. We show that the alternating direction method is very efficient for solving image restoration and reconstruction problems.<\/jats:p>","DOI":"10.1137\/090774823","type":"journal-article","created":{"date-parts":[[2010,8,31]],"date-time":"2010-08-31T18:25:08Z","timestamp":1283279108000},"page":"2710-2736","source":"Crossref","is-referenced-by-count":211,"title":["Solving Constrained Total-variation Image Restoration and Reconstruction Problems via Alternating Direction Methods"],"prefix":"10.1137","volume":"32","author":[{"given":"Michael K.","family":"Ng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierre","family":"Weiss","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoming","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,8,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-004-0812-z"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-005-4783-8"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-005-4948-3"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-006-4331-z"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1109\/79.581363"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596299767"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1109\/42.241890"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997327075"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2004.832922"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/050626090"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1109\/JSTSP.2007.910264"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2004.12.004"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1956-0084194-4"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01581204"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"J. 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