Oymak, Samet and Hassibi, Babak
(2012)
*Recovering Jointly Sparse Signals via Joint Basis Pursuit.*
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(Unpublished)
http://resolver.caltech.edu/CaltechAUTHORS:20150126-075526346

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## Abstract

This work considers recovery of signals that are sparse over two bases. For instance, a signal might be sparse in both time and frequency, or a matrix can be low rank and sparse simultaneously. To facilitate recovery, we consider minimizing the sum of the ℓ_1-norms that correspond to each basis, which is a tractable convex approach. We find novel optimality conditions which indicates a gain over traditional approaches where ℓ_1 minimization is done over only one basis. Next, we analyze these optimality conditions for the particular case of time-frequency bases. Denoting sparsity in the first and second bases by k_1,k_2 respectively, we show that, for a general class of signals, using this approach, one requires as small as O(max{k_1,k_2} log log n) measurements for successful recovery hence overcoming the classical requirement of Θ(min{k_1,k_2} log (n/(min{k_1,k_2})) for ℓ _1 minimization when k_1 ≈ k_2. Extensive simulations show that, our analysis is approximately tight.

Item Type: | Report or Paper (Discussion Paper) | ||||||||||||
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Additional Information: | 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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Subject Keywords: | basis pursuit, compressed sensing, phase re- trieval, duality, convex optimization | ||||||||||||

Record Number: | CaltechAUTHORS:20150126-075526346 | ||||||||||||

Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20150126-075526346 | ||||||||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||

ID Code: | 54054 | ||||||||||||

Collection: | CaltechAUTHORS | ||||||||||||

Deposited By: | Shirley Slattery | ||||||||||||

Deposited On: | 26 Jan 2015 18:55 | ||||||||||||

Last Modified: | 26 Jan 2015 18:55 |

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