Certifying the restricted isometry property is hard

Details Certifying the restricted isometry property is hard Certifying the restricted isometry property is hard

2012-04-06

arxiv.org/abs/1204.1580v1

Mathematics

Functional Analysis

7 pages

Scientific paper

This paper is concerned with an important matrix condition in compressed sensing known as the restricted isometry property (RIP). We demonstrate that testing whether a matrix satisfies RIP is hard for NP under randomized polynomial-time reductions. Our reduction is from the NP-complete clique decision problem, and it uses ideas from matroid theory. As a consequence of our result, it is impossible to efficiently test for RIP provided NP \not\subseteq BPP, an assumption which is slightly stronger than P \neq NP.

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