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Rick Chartrand and Wotao Yin, "Iteratively reweighted algorithms for compressive sensing", in 33rd International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2008

Abstract

The theory of compressive sensing has shown that sparse signals can be reconstructed exactly from remarkably few measurements. In [Chartrand, 2007], it was shown empirically that using p minimization with p < 1 can do so with fewer measurements than with p=1. In this paper we consider the use of iteratively reweighted algorithms for computing local minima of the nonconvex problem. In particular, a particular regularization strategy is found to greatly improve the ability of a reweighted least-squares algorithm to recover sparse signals, with exact recovery being observed for signals that are much less sparse than required by an unregularized version (such as FOCUSS, [Rao, 1999]). Improvements are also observed for the reweighted-1 approach of Candès, Wakin, and Boyd.

BibTeX Entry

@inproceedings{chartrand-2008-iteratively,
author = {Rick Chartrand and Wotao Yin},
title = {Iteratively reweighted algorithms for compressive sensing},
year = {2008},
urlpdf = {http://math.lanl.gov/Research/Publications/Docs/chartrand-2008-iteratively.pdf},
booktitle = {33rd International Conference on Acoustics, Speech, and Signal Processing (ICASSP)}
}