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Iteratively reweighted algorithms for compressive sensing

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2 Author(s)
Chartrand, R. ; Los Alamos Nat. Lab., Los Alamos, NM, USA ; Wotao Yin

The theory of compressive sensing has shown that sparse signals can be reconstructed exactly from many fewer measurements than traditionally believed necessary. In [1], it was shown empirically that using lscrp 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, [2]). Improvements are also observed for the reweighted-lscr1 approach of [3].

Published in:

Acoustics, Speech and Signal Processing, 2008. ICASSP 2008. IEEE International Conference on

Date of Conference:

March 31 2008-April 4 2008

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