Certifying the restricted isometry property is hard

Afonso S. Bandeira, Edgar Dobriban, Dustin G. Mixon, William F. Sawin

Research output: Contribution to journalArticlepeer-review

170 Scopus citations


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= NP.

Original languageEnglish (US)
Article number6478822
Pages (from-to)3448-3450
Number of pages3
JournalIEEE Transactions on Information Theory
Issue number6
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


  • Compressed sensing
  • computational complexity
  • restricted isometry property


Dive into the research topics of 'Certifying the restricted isometry property is hard'. Together they form a unique fingerprint.

Cite this