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Deterministic phase guarantees for robust recovery in incoherent dictionaries

Li, Cheuk Ting and Oymak, Samet and Hassibi, Babak (2012) Deterministic phase guarantees for robust recovery in incoherent dictionaries. In: 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE , Piscataway, NJ, pp. 3817-3820. ISBN 978-1-4673-0045-2.

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This paper presents a relaxation of an assumption usually imposed in the recovery of sparse vectors with random support in pairs of orthonormal bases or incoherent dictionaries by basis pursuit. The assumption requires the phases of the entries of the sparse vector to be chosen randomly in [0, 2π). This paper provides probabilistic recovery guarantees for deterministic phases. We prove that, if a phase pattern is fixed, then a sparse vector with random support and corresponding phases can be recovered with high probability. As a result, the phases can take any distribution and can be dependent, as long as they are independent of the support. Furthermore, this improvement does not come at the expense of the maximum recoverable sparsity.

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Additional Information:© 2012 IEEE. This work was supported in part by the National Science Foundation under grants CCF-0729203, CNS-0932428 and CCF-1018927., by the Office of Naval Research under the MURI grant N00014-08-1-0747, and by Caltech’s Lee Center for Advanced Networking. This work was performed while the first author was an exchange student at the California Institute of Technology, supported by Professor Charles K. Kao Research Exchange Scholarship of The Chinese University of Hong Kong.
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Office of Naval Research (ONR)N00014-08-1-0747
Caltech’s Lee Center for Advanced NetworkingUNSPECIFIED
Subject Keywords:uncertainty principle, basis pursuit, sparsity, duality in optimization, incoherent dictionary
Record Number:CaltechAUTHORS:20150224-072653860
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55130
Deposited By: Shirley Slattery
Deposited On:25 Feb 2015 01:16
Last Modified:10 Nov 2021 20:41

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