Foundations of Computational Mathematics

, Volume 9, Issue 3, pp 317–334

Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit

Article

DOI: 10.1007/s10208-008-9031-3

Cite this article as:
Needell, D. & Vershynin, R. Found Comput Math (2009) 9: 317. doi:10.1007/s10208-008-9031-3

Abstract

This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements—L1-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 L1-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 approximation 

Mathematics Subject Classification (2000)

68W20 65T50 41A46 

Copyright information

© SFoCM 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaDavisUSA

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