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Enhancing Sparsity by Reweighted ℓ1 Minimization (2007)
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| Citations: | 145 - 4 self |
BibTeX
@MISC{Candès07enhancingsparsity,
author = {Emmanuel J. Candès and Michael B. Wakin and Stephen P. Boyd},
title = {Enhancing Sparsity by Reweighted ℓ1 Minimization},
year = {2007}
}
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Abstract
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained ℓ1 minimization. In this paper, we study a novel method for sparse signal recovery that in many situations outperforms ℓ1 minimization in the sense that substantially fewer measurements are needed for exact recovery. The algorithm consists of solving a sequence of weighted ℓ1-minimization problems where the weights used for the next iteration are computed from the value of the current solution. We present a series of experiments demonstrating the remarkable performance and broad applicability of this algorithm in the areas of sparse signal recovery, statistical estimation, error correction and image processing. Interestingly, superior gains are also achieved when our method is applied to recover signals with assumed near-sparsity in overcomplete representations—not by reweighting the ℓ1 norm of the coefficient sequence as is common, but by reweighting the ℓ1 norm of the transformed object. An immediate consequence is the possibility of highly efficient data acquisition protocols by improving on a technique known as compressed sensing.
Keyphrases
sparse signal recovery coefficient sequence superior gain current solution statistical estimation remarkable performance image processing error correction efficient data acquisition protocol compressed sensing algorithm consists exact recovery many situation transformed object immediate consequence broad applicability next iteration overcomplete representation assumed near-sparsity linear measurement weighted 1-minimization problem incomplete set sparse signal novel method
