A simple proof of the restricted isometry property for random matrices
| dc.citation.bibtexName | article | |
| dc.citation.journalTitle | Constructive Approximation | |
| dc.contributor.author | Baraniuk, Richard G. | |
| dc.contributor.author | Davenport, Mark A. | |
| dc.contributor.author | DeVore, Ronald A. | |
| dc.contributor.author | Wakin, Michael B. | |
| dc.date.accessioned | 2008-08-19T04:22:43Z | |
| dc.date.available | 2008-08-19T04:22:43Z | |
| dc.date.issued | 2007-01-18 | en |
| dc.description.abstract | We give a simple technique for verifying the Restricted Isometry Property (as introduced by Candès and Tao) for random matrices that underlies Compressed Sensing. Our approach has two main ingredients: (i) concentration inequalities for random inner products that have recently provided algorithmically simple proofs of the Johnson–Lindenstrauss lemma; and (ii) covering numbers for finite-dimensional balls in Euclidean space. This leads to an elementary proof of the Restricted Isometry Property and brings out connections between Compressed Sensing and the Johnson–Lindenstrauss lemma. As a result, we obtain simple and direct proofs of Kashin’s theorems on widths of finite balls in Euclidean space (and their improvements due to Gluskin) and proofs of the existence of optimal Compressed Sensing measurement matrices. In the process, we also prove that these measurements have a certain universality with respect to the sparsity-inducing basis. | en |
| dc.description.sponsorship | This research was supported by Office of Naval Research grants ONR N00014-03-1-0051, ONR/ DEPSCoR N00014-03-1-0675, ONR/DEPSCoR N00014-00-1-0470, and ONR N00014-02-1-0353; Army Research Office contract DAAD 19-02-1-0028; AFOSR grants UF/USAF F49620-03-1-0381 and FA9550- 04-0148; DARPA grant N66001-06-1-2011; NSF grants DMS-354707, CCF-0431150, CNS-0435425, and CNS-0520280; and the Texas Instruments Leadership University Program. | en |
| dc.identifier.citation | R. G. Baraniuk, M. A. Davenport, R. A. DeVore and M. B. Wakin, "A simple proof of the restricted isometry property for random matrices," <i>Constructive Approximation,</i> 2007. | |
| dc.identifier.doi | http://dx.doi.org/10.1007/s00365-007-9003-x | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/21683 | |
| dc.language.iso | eng | |
| dc.subject | compressed sensing | en |
| dc.subject | sampling | en |
| dc.subject | random matrices | en |
| dc.subject | concentration inequalities | en |
| dc.title | A simple proof of the restricted isometry property for random matrices | en |
| dc.title.alternative | The Johnson-Lindenstrauss lemma meets compressed sensing | en |
| dc.type | Journal article | |
| dc.type.dcmi | Text |