An Alternating l1 approach to the compressed sensing problem

Details An Alternating l1 approach to the compressed sensing problem An Alternating l1 approach to the compressed sensing problem

2008-09-03

arxiv.org/abs/0809.0660v3

IEEE Signal Processing Letters, Feb. 2010 Volume : 17 , Issue: 2 On page(s): 181 - 184

Statistics

Methodology

7 pages, 1 figure, presented at ICIAM 07

Scientific paper

Compressed sensing is a new methodology for constructing sensors which allow sparse signals to be efficiently recovered using only a small number of observations. The recovery problem can often be stated as the one of finding the solution of an underdetermined system of linear equations with the smallest possible support. The most studied relaxation of this hard combinatorial problem is the $l_1$-relaxation consisting of searching for solutions with smallest $l_1$-norm. In this short note, based on the ideas of Lagrangian duality, we introduce an alternating $l_1$ relaxation for the recovery problem enjoying higher recovery rates in practice than the plain $l_1$ relaxation and the recent reweighted $l_1$ method of Cand\`es, Wakin and Boyd.

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