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Abstract: We consider the problem of estimating a deterministic sparse vector x fromunderdetermined measurements Ax+w, where w represents white Gaussian noise andA is a given deterministic dictionary. We analyze the performance of threesparse estimation algorithms: basis pursuit denoising BPDN, orthogonalmatching pursuit OMP, and thresholding. These algorithms are shown to achievenear-oracle performance with high probability, assuming that x is sufficientlysparse. Our results are non-asymptotic and are based only on the coherence ofA, so that they are applicable to arbitrary dictionaries. Differences in theprecise conditions required for the performance guarantees of each algorithmare manifested in the observed performance at high and low signal-to-noiseratios. This provides insight on the advantages and drawbacks of convexrelaxation techniques such as BPDN as opposed to greedy approaches such as OMPand thresholding.



Autor: Zvika Ben-Haim, Yonina C. Eldar, Michael Elad

Fuente: https://arxiv.org/







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