General constructions of deterministic (S)RIP matrices for compressive sampling

Arya Mazumdar, Alexander Barg

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

7 Scopus citations

Abstract

Compressive sampling is a technique of recovering sparse N-dimensional signals from low-dimensional sketches, i.e., their linear images in ℝm, m ≪ N. The main question associated with this technique is construction of linear operators that allow faithful recovery of the signal from its sketch. The most frequently used sufficient condition for robust recovery is the near-isometry property of the operator when restricted to k-sparse signals. We study 1-matrices of dimensions m × N that satisfy the restricted isometry property of order k (k-RIP). As our main set of results, we describe a general method of constructing sampling matrices for which a statistical version of k-RIP holds. We also show that mN matrices with k-RIP and m = O(k2 logN) can be constructed with time complexity O(k 2N logN).

Original languageEnglish (US)
Title of host publication2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Pages678-682
Number of pages5
DOIs
StatePublished - 2011
Event2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, Russian Federation
Duration: Jul 31 2011Aug 5 2011

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8104

Other

Other2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
CountryRussian Federation
CitySt. Petersburg
Period7/31/118/5/11

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