Coherence analysis of iterative thresholding algorithms

Authors:
Arian Maleki
Affiliations:
Department of Electrical Engineering and Statistics, Stanford University
Venue:
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Year:
2009

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Abstract

There is a recent surge of interest in developing algorithms for finding sparse solutions of underdetermined systems of linear equations y = φx. In many applications, extremely large problem sizes are envisioned, with at least tens of thousands of equations and hundreds of thousands of unknowns. For such problem sizes, low computational complexity is paramount. The best studied l1 minimization algorithm is not fast enough to fulfill this need. Iterative thresholding algorithms have been proposed to address this problem. In this paper we want to analyze three of these algorithms theoretically, and give sufficient conditions under which they recover the sparsest solution.