Coherence-based near-oracle performance guarantees for sparse estimation under Gaussian noise

Abstract : We consider the problem of estimating a deterministic sparse vector x0 from underdetermined measurements Ax0 + w, where w represents white Gaussian noise and A is a given deterministic dictionary. We analyze the performance of three sparse estimation algorithms: basis pursuit denoising, orthogonal matching pursuit, and thresholding. These approaches are shown to achieve near-oracle performance with high probability, assuming that x0 is sufficiently sparse. Our results are non-asymptotic and are based only on the coherence of A, so that they are applicable to arbitrary dictionaries.
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Acoustics Speech and Signal Processing (ICASSP), 2010 IEEE International Conference on, Mar 2010, dallas, United States. pp.3590 -3593, 2010, 〈10.1109/ICASSP.2010.5495919〉
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https://hal.inria.fr/inria-00569084
Contributeur : Jules Espiau de Lamaestre <>
Soumis le : jeudi 24 février 2011 - 11:32:21
Dernière modification le : jeudi 24 février 2011 - 11:32:21

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Zvika Ben-Haim, Yonina C. Eldar, Michael Elad. Coherence-based near-oracle performance guarantees for sparse estimation under Gaussian noise. Acoustics Speech and Signal Processing (ICASSP), 2010 IEEE International Conference on, Mar 2010, dallas, United States. pp.3590 -3593, 2010, 〈10.1109/ICASSP.2010.5495919〉. 〈inria-00569084〉

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