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Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit

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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.

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Authors and Affiliations

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

    Deanna Needell & Roman Vershynin

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  1. Deanna Needell
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  2. Roman Vershynin
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Correspondence to Roman Vershynin.

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Communicated by Emmanuel Candès.

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Needell, D., Vershynin, R. Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit. Found Comput Math 9, 317–334 (2009). https://doi.org/10.1007/s10208-008-9031-3

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  • DOI: https://doi.org/10.1007/s10208-008-9031-3

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