Iteratively reweighted algorithms for compressive sensing

Rick Chartrand Wotao Yin

Optimization and Control mathscidoc:1912.43769

3869-3872, 2008.3
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 lscr<sup>p</sup> minimization with p &lt; 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-lscr<sup>1</sup> approach of [3].
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  title={Iteratively reweighted algorithms for compressive sensing},
  author={Rick Chartrand, and Wotao Yin},
Rick Chartrand, and Wotao Yin. Iteratively reweighted algorithms for compressive sensing. 2008. pp.3869-3872.
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