Uniform Uncertainty Principle and signal recovery via Regularized Orthogonal Matching Pursuit

Details Uniform Uncertainty Principle and signal recovery via Regularized Orthogonal Matching Pursuit Uniform Uncertainty Principle and signal recovery via Regularized Orthogonal Matching Pursuit

2007-07-28

arxiv.org/abs/0707.4203v4

Mathematics

Numerical Analysis

This is the final version of the paper, including referee suggestions

Scientific paper

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 the Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of the L_1-minimization. Our algorithm ROMP reconstructs a sparse signal in a number of iterations linear in the sparsity (in practice even logarithmic), and the reconstruction is exact provided the linear measurements satisfy the Uniform Uncertainty Principle.

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