Sparse recovery properties of statistical RIP matrices

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 R m, 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. In this paper we study performance of standard sparse recovery algorithms in the situation when the sampling matrices satisfy statistical isometry properties. Namely, we show it is possible to recover a sparse signal from its sketch with high probability using the basis pursuit algorithm. Moreover, the same statistical isometry conditions are sufficient for robust model selection with the Lasso algorithm. Finally we show that matrices with the needed properties can be constructed from binary error-correcting codes.

Original languageEnglish (US)
Title of host publication2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011
Pages9-12
Number of pages4
DOIs
StatePublished - 2011
Event2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011 - Monticello, IL, United States
Duration: Sep 28 2011Sep 30 2011

Publication series

Name2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011

Other

Other2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011
CountryUnited States
CityMonticello, IL
Period9/28/119/30/11

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