Certifying the restricted isometry property is hard

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

doi:10.1109/TIT.2013.2248414

Certifying the restricted isometry property is hard

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

Mathematics

Research output: Contribution to journal › Article › peer-review

187 Scopus citations

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= NP.

Original language	English (US)
Article number	6478822
Pages (from-to)	3448-3450
Number of pages	3
Journal	IEEE Transactions on Information Theory
Volume	59
Issue number	6
DOIs	https://doi.org/10.1109/TIT.2013.2248414
State	Published - 2013

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

Keywords

Compressed sensing
computational complexity
restricted isometry property

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10.1109/TIT.2013.2248414

Cite this

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title = "Certifying the restricted isometry property is hard",

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= NP.",

keywords = "Compressed sensing, computational complexity, restricted isometry property",

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AU - Dobriban, Edgar

AU - Mixon, Dustin G.

AU - Sawin, William F.

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AB - 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.

KW - Compressed sensing

KW - computational complexity

KW - restricted isometry property

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Certifying the restricted isometry property is hard

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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