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Sparse Recovery From Multiple Measurement Vectors Using Exponentiated Gradient Updates

Khanna, Saurabh and Murthy, Chandra Ramabhadra (2018) Sparse Recovery From Multiple Measurement Vectors Using Exponentiated Gradient Updates. In: IEEE SIGNAL PROCESSING LETTERS, 25 (10). pp. 1485-1489.

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Official URL: http://dx.doi.org/10.1109/LSP.2018.2865672

Abstract

In this letter, we address the problem of reconstructing the common nonzero support of multiple joint sparse vectors from their noisy and underdetermined linear measurements. The support recovery problem is formulated as the selection of non-negative hyperparameters of a correlation-aware, joint sparsity inducing Gaussian prior. The hyperparameters are recovered as a non-negative sparse solution of covariance-matching constraints formulated in the observation space by solving a sequence of proximal regularized convex optimization problems. For proximal regularization based on Von Neumann Bregman matrix divergence, an exponentiated gradient (EG) update is proposed, which when applied iteratively, converges to hyperparameters with the correct sparse support. Compared to existing multiple measurement vector support recovery algorithms, the proposed multiplicative EG update has a significantly lower computational and storage complexity and takes fewer iterations to converge. We empirically demonstrate that the support-recovery algorithm based on the proposed EG update can solve million variable support recovery problems in tens of seconds. Additionally, by leveraging its correlation-awareness property, the proposed algorithm can recover supports of size as high as O(m(2)) from only m linear measurements per joint sparse vector.

Item Type: Journal Article
Additional Information: Copy right for this article belong to IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 445 HOES LANE, PISCATAWAY, NJ 08855-4141 USA
Keywords: Compressive sensing; covariance matching; exponentiated gradient (EG) updates; joint sparsity; multiple measurement vectors; sparse recovery; Von Neumann divergence
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Depositing User: Id for Latest eprints
Date Deposited: 15 Sep 2018 15:51
Last Modified: 15 Sep 2018 15:51
URI: http://eprints.iisc.ac.in/id/eprint/60679

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