Uniform Uncertainty Principle and signal recovery via Regularized Orthogonal Matching Pursuit

Deanna Needell; Roman Vershynin

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arXiv · 0707.4203

Uniform Uncertainty Principle and signal recovery via Regularized Orthogonal Matching Pursuit

Deanna Needell·Roman Vershynin

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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 -- 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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Deanna Needell, Roman Vershynin. 2008-03-15. Uniform Uncertainty Principle and signal recovery via Regularized Orthogonal Matching Pursuit. https://arxiv.org/abs/0707.4203

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