Recovering Jointly Sparse Signals via Joint Basis Pursuit
- Creators
- Oymak, Samet
- Hassibi, Babak
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.
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.Attached Files
Submitted - Recovering_Jointly_Sparse_Signals_via_Joint_Basis_Pursuit.pdf
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Additional details
- Eprint ID
- 54054
- Resolver ID
- CaltechAUTHORS:20150126-075526346
- NSF
- CCF-0729203
- NSF
- CNS-0932428
- NSF
- CCF-1018927
- Office of Naval Research (ONR)
- N00014-08-1-0747
- Caltech's Lee Center for Advanced Networking
- Created
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2015-01-26Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field