An Alternating l(1) Approach to the Compressed Sensing Problem

作者：Chretien Stephane^*

来源：IEEE Signal Processing Letters, 2010, 17(2): 181-184.

DOI：10.1109/LSP.2009.2034554

• Compressed sensing
• exact recovery
• Lagrangian relaxation
• NP-hard optimization problems
• l(1) relaxation
• reweighted l(1) relaxation

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 some recent improvements of this relaxation.

• 出版日期2010-2