Sparse Recovery From Multiple Measurement Vectors Using Exponentiated Gradient Updates

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 nonnegative hyperparameters of a correlation-aware, joint spar...

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Bibliographic Details
Published in:IEEE signal processing letters Vol. 25; no. 10; pp. 1485 - 1489
Main Authors: Khanna, Saurabh, Murthy, Chandra Ramabhadra
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Compressive sensing
Computational geometry
Convergence
Convexity
Covariance
covariance matching
Covariance matrices
Divergence
exponentiated gradient (EG) updates
joint sparsity
multiple measurement vectors
Noise measurement
Optimization
Recovery
Regularization
Sensors
Signal processing algorithms
Size measurement
Sparse matrices
sparse recovery
Symmetric matrices
Von Neumann divergence
ISSN:1070-9908, 1558-2361
Online Access:Get full text
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Summary: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 nonnegative hyperparameters of a correlation-aware, joint sparsity inducing Gaussian prior. The hyperparameters are recovered as a nonnegative 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.
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ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2018.2865672