Article

Foundations of Computational Mathematics

, Volume 9, Issue 3, pp 317-334

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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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