Foundations of Computational Mathematics
, Volume 9, Issue 3, pp 317334
First online:
Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
 Deanna NeedellAffiliated withDepartment of Mathematics, University of California
 , Roman VershyninAffiliated withDepartment of Mathematics, University of California Email author
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This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements—L_{1}minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L_{1}minimization. Our algorithm, ROMP, reconstructs a sparse signal in a number of iterations linear in the sparsity, and the reconstruction is exact provided the linear measurements satisfy the uniform uncertainty principle.
Keywords
Signal recovery algorithms Restricted isometry condition Uncertainty principle Basis pursuit Compressed sensing Orthogonal matching pursuit Signal recovery Sparse approximationMathematics Subject Classification (2000)
68W20 65T50 41A46 Title
 Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
 Journal

Foundations of Computational Mathematics
Volume 9, Issue 3 , pp 317334
 Cover Date
 200906
 DOI
 10.1007/s1020800890313
 Print ISSN
 16153375
 Online ISSN
 16153383
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Signal recovery algorithms
 Restricted isometry condition
 Uncertainty principle
 Basis pursuit
 Compressed sensing
 Orthogonal matching pursuit
 Signal recovery
 Sparse approximation
 68W20
 65T50
 41A46
 Industry Sectors
 Authors

 Deanna Needell ^{(1)}
 Roman Vershynin ^{(1)}
 Author Affiliations

 1. Department of Mathematics, University of California, One Shields Ave, Davis, CA, 95616, USA