English

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}
}
R2 v1 2026-06-21T20:45:57.647Z