Certifying the restricted isometry property is hard
Functional Analysis
2017-10-03 v2 Computational Complexity
Information Theory
math.IT
Abstract
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 NP-hard. As a consequence of our result, it is impossible to efficiently test for RIP provided P \neq NP.
Cite
@article{arxiv.1204.1580,
title = {Certifying the restricted isometry property is hard},
author = {Afonso S. Bandeira and Edgar Dobriban and Dustin G. Mixon and William F. Sawin},
journal= {arXiv preprint arXiv:1204.1580},
year = {2017}
}