Exact optimization for the l1-Compressive Sensing problem using a modified Dantzig-Wolfe method

Authors:
Alexandre Borghi;Jérôme Darbon;Sylvain Peyronnet
Affiliations:
Univ Paris-Sud, UMR8623, LRI, Orsay, F-91405, France;CMLA, ENS Cachan, CNRS, PRES UniverSud, F-94230, France;Univ Paris-Sud, UMR8623, LRI, Orsay, F-91405, France
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

This paper considers the l^1-Compressive Sensing problem and presents an efficient algorithm that computes an exact solution. The idea consists in reformulating the problem such that it yields a modified Dantzig-Wolfe decomposition that allows to efficiently apply all standard simplex pivoting rules. Experimental results show the superiority of our approach compared to standard linear programming methods.