Testing the Nullspace Property using Semidefinite Programming

Details Testing the Nullspace Property using Semidefinite Programming Testing the Nullspace Property using Semidefinite Programming

2008-07-22

arxiv.org/abs/0807.3520v6

Mathematics

Optimization and Control

Some typos corrected in Section 4.2

Scientific paper

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 either rely on computing sparse eigenvalues of the design matrix or on properties of its nullspace. So far, no tractable algorithm is known to test these conditions and most current results rely on asymptotic properties 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.

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