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Weighted compressed sensing and rank minimization

Oymak, Samet and Khajehnejad, M. Amin and Hassibi, Babak (2011) Weighted compressed sensing and rank minimization. In: 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE , Piscataway, NJ, pp. 3736-3739. ISBN 978-1-4577-0538-0.

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We present an alternative analysis of weighted ℓ_1 minimization for sparse signals with a nonuniform sparsity model, and extend our results to nuclear norm minimization for matrices with nonuniform singular vector distribution. In the case of vectors, we find explicit upper bounds for the successful recovery thresholds, and give a simple suboptimal weighting rule. For matrices, the thresholds we find are only implicit, and the optimal weight selection requires an exhaustive search. For the special case of very wide matrices, the relationship is made explicit and the optimal weight assignment is the same as the vector case. We demonstrate through simulations that for vectors, the suggested weighting scheme improves the recovery performance over that of regular ℓ_1 minimization.

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Additional Information:© 2011 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.
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Office of Naval Research (ONR)N00014-08-1-0747
Caltech Lee Center for Advanced NetworkingUNSPECIFIED
Record Number:CaltechAUTHORS:20150204-071344814
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54343
Deposited By: Shirley Slattery
Deposited On:05 Feb 2015 00:54
Last Modified:03 Oct 2019 07:57

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