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 algorithmsRestricted isometry conditionUncertainty principleBasis pursuitCompressed sensingOrthogonal matching pursuitSignal recoverySparse approximation

Mathematics Subject Classification (2000)

68W2065T5041A46

Copyright information

© SFoCM 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaDavisUSA