Testing the Nullspace Property using Semidefinite Programming

Download: http://arxiv.org/abs/0807.3520.

Authors: A. d’Aspremont and L. El Ghaoui.

Status: Preprint on arXiv, to be submitted to Math. Progr., December 2008.

Abstract: Recent results in compressed sensing show that, under certain conditions, the sparsest solution to an underdetermined set of linear equations can be recovered by solving a linear program. These results rely on nullspace properties of the system matrix. So far, no tractable algorithm is known to test these conditions and most current results rely on asymptotic properties of sparse eigenvalues of random matrices. Given a matrix A, we use semidefinite relaxation techniques to test the nullspace property on A and show on some numerical examples that these relaxation bounds can prove perfect recovery of sparse solutions with relatively high cardinality.

Bibtex reference:

@unpublished{AsE:08,
	Author = {A. {d'Aspremont} and L. {El Ghaoui}},
	Month = {February},
	Note = {arXiv:0807.3520},
	Title = {Testing the Nullspace Property using Semidefinite
	Programming},
	Note = {Submitted to {\em Math. Progr.,} special issue on Machine 	Learning},
	Year = {2008}}