NESTA: A Fast and Accurate First-Order Method for Sparse Recovery

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NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
Abstract. Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by recent breakthroughs in the development of novel first-order methods in convex optimization, most notably Nesterov’s smoothing technique, this paper introduces a fast and accurate algorithm for solving common recovery problems in signal processing. In the spirit of Nesterov’s work, one of the key ideas of this algorithm is a subtle averaging of sequences of iterates, which has been shown to improve the convergence properties of standard gradient-descent algorithms. This paper 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...
Stephen Becker, Jérôme Bobin, Emmanue
Added 15 May 2011
Updated 15 May 2011
Type Journal
Year 2011
Authors Stephen Becker, Jérôme Bobin, Emmanuel J. Candès
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