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Recently several successful studies of approximating this model and subsequently finding fast algorithms were conducted which have partially solved this problem. The aim of this paper is to generalize a fast multilevel denoising method to solving the minimization model for simultaneously denoising and deblurring. Our new idea is to overcome the complexity issue by a detailed study of the structured matrices that are associated with the blurring operator. A fast algorithm can then be obtained for directly solving the variational model. Supporting numerical experiments on gray scale images are presented.<\/jats:p>","DOI":"10.1137\/080741410","type":"journal-article","created":{"date-parts":[[2010,3,31]],"date-time":"2010-03-31T18:18:15Z","timestamp":1270059495000},"page":"1043-1063","source":"Crossref","is-referenced-by-count":22,"title":["A Multilevel Algorithm for Simultaneously Denoising and Deblurring Images"],"prefix":"10.1137","volume":"32","author":[{"given":"Raymond H.","family":"Chan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ke","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,3,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/10\/6\/003"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0729052"},{"key":"R3","unstructured":"H. C. Andrews and B. R. 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