Subspace weighted ℓ2,1 minimization for sparse signal recovery
In this article, we propose a weighted ℓ 2,1 minimization algorithm for jointly-sparse signal recovery problem. The proposed algorithm exploits the relationship between the noise subspace and the overcomplete basis matrix for designing weights, i.e., large weights are appointed to the entries, whose...
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Published in | EURASIP journal on advances in signal processing Vol. 2012; no. 1; p. 98 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Cham
Springer International Publishing
02.05.2012
BioMed Central Ltd |
Subjects | |
Online Access | Get full text |
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Summary: | In this article, we propose a weighted
ℓ
2,1
minimization algorithm for jointly-sparse signal recovery problem. The proposed algorithm exploits the relationship between the noise subspace and the overcomplete basis matrix for designing weights, i.e., large weights are appointed to the entries, whose indices are more likely to be outside of the row support of the jointly sparse signals, so that their indices are expelled from the row support in the solution, and small weights are appointed to the entries, whose indices correspond to the row support of the jointly sparse signals, so that the solution prefers to reserve their indices. Compared with the regular
ℓ
2,1
minimization, the proposed algorithm can not only further enhance the sparseness of the solution but also reduce the requirements on both the number of snapshots and the signal-to-noise ratio (SNR) for stable recovery. Both simulations and experiments on real data demonstrate that the proposed algorithm outperforms the
ℓ
1
-SVD algorithm, which exploits straightforwardly
ℓ
2,1
minimization, for both deterministic basis matrix and random basis matrix. |
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ISSN: | 1687-6180 1687-6180 |
DOI: | 10.1186/1687-6180-2012-98 |