Greedy signal recovery and uncertainty principles

Deanna Needell; Roman Vershynin

doi:10.1117/12.776996

20 March 2008 Greedy signal recovery and uncertainty principles

Deanna Needell, Roman Vershynin

Proceedings Volume 6814, Computational Imaging VI; 68140J (2008) https://doi.org/10.1117/12.776996
Event: Electronic Imaging, 2008, San Jose, California, United States

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 the Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of the 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. In the case of inaccurate measurements and approximately sparse signals, the noise level of the recovery is proportional to &sqrt;log n parallel e parallel ₂ where e is the error vector.

Citation Download Citation

Deanna Needell and Roman Vershynin "Greedy signal recovery and uncertainty principles", Proc. SPIE 6814, Computational Imaging VI, 68140J (20 March 2008); https://doi.org/10.1117/12.776996

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