On the restricted isometry of deterministically subsampled Fourier matrices

Jarvis Haupt, Lorne Applebaum, Robert Nowak

Research output: Chapter in Book/Report/Conference proceedingConference contribution

32 Scopus citations

Abstract

Matrices satisfying the Restricted Isometry Property (RIP) are central to the emerging theory of compressive sensing (CS). Initial results in CS established that the recovery of sparse vectors x from a relatively small number of linear observations of the form y = Ax can be achieved, using a tractable convex optimization, whenever A is a matrix that satisfies the RIP; similar results also hold when x is nearly sparse or the observations are corrupted by noise. In contrast to random constructions prevalent in many prior works in CS, this paper establishes a collection of deterministic matrices, formed by deterministic selection of rows of Fourier matrices, which satisfy the RIP. Implications of this result for the recovery of signals having sparse spectral content over a large bandwidth are discussed.

Original languageEnglish (US)
Title of host publication2010 44th Annual Conference on Information Sciences and Systems, CISS 2010
DOIs
StatePublished - Jun 24 2010
Event44th Annual Conference on Information Sciences and Systems, CISS 2010 - Princeton, NJ, United States
Duration: Mar 17 2010Mar 19 2010

Publication series

Name2010 44th Annual Conference on Information Sciences and Systems, CISS 2010

Other

Other44th Annual Conference on Information Sciences and Systems, CISS 2010
CountryUnited States
CityPrinceton, NJ
Period3/17/103/19/10

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