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...

• Type: Journal
• Year: 2011
• Where: SIAMIS
• Authors: Stephen Becker, Jérôme Bobin, Emmanuel J. Candès
• Keywords: Algorithm, Compressed Sensing, Problems, SIAMIS 2011, Software Engineering