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Enhancing Sparsity by Reweighted l 1 Minimization by Emmanuel J. Candès; Michael B. Wakin; Stephen P. Boyd is a Mathematics article available to read on EtoBox.

What is Enhancing Sparsity by Reweighted l 1 Minimization about?

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 1 minimization. In this paper, we study a novel method for sparse signal recovery that in many situations outperforms 1 minimization in the sense that substantially fewer measurements are needed for exact recovery. The algorithm consists of solving a sequence of weighted 1 -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 1 norm of the coefficient sequence as is common, but by reweighting the 1 norm of the transformed object. An immediate consequence is the possibility of highly efficient data acquisition protocols by impro

Who reads Enhancing Sparsity by Reweighted l 1 Minimization?

Author

Emmanuel J. Candès; Michael B. Wakin; Stephen P. Boyd

Publisher

SP Birkhäuser Verlag Boston; Springer-Verlag; Birkhauser Boston; Springer Science and Business Media LLC; Springer Nature (ISSN 1069-5869)

Published

2008

Language

EN

Field

Mathematics (Physical Sciences)