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A, 103 (2005), pp. 127\u2013152], and demonstrates that this approach is ideally suited for solving large-scale compressed sensing reconstruction problems as (1) it is computationally efficient, (2) it is accurate and returns solutions with several correct digits, (3) it is flexible and amenable to many kinds of reconstruction problems, and (4) it is robust in the sense that its excellent performance across a wide range of problems does not depend on the fine tuning of several parameters. Comprehensive numerical experiments on realistic signals exhibiting a large dynamic range show that this algorithm compares favorably with recently proposed state-of-the-art methods. We also apply the algorithm to solve other problems for which there are fewer alternatives, such as total-variation minimization and convex programs seeking to minimize the $\\ell_1$ norm of $Wx$ under constraints, in which W is not diagonal. The code is available online as a free package in the MATLAB language.<\/jats:p>","DOI":"10.1137\/090756855","type":"journal-article","created":{"date-parts":[[2011,1,7]],"date-time":"2011-01-07T18:25:52Z","timestamp":1294424752000},"page":"1-39","source":"Crossref","is-referenced-by-count":765,"title":["NESTA: A Fast and Accurate First-Order Method for Sparse Recovery"],"prefix":"10.1137","volume":"4","author":[{"given":"Stephen","family":"Becker","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00e9r\u00f4me","family":"Bobin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Emmanuel J.","family":"Cand\u00e8s","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,1,6]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2010.2047910"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-009-0149-y"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/8.1.141"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/080716542"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2007.909319"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623497330963"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"J. 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Darbon and M. Sigelle,\n                      A fast and exact algorithm for total-variation minimization\n                      , in Proceedings of the 2nd Iberian Conference on Pattern Recognition and Image Analysis (IbPRIA), Lecture Notes in Comput. 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