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Entropy 2019, 21(3), 247; https://doi.org/10.3390/e21030247

Bayesian Compressive Sensing of Sparse Signals with Unknown Clustering Patterns

Electrical and Computer Engineering Department and Information Dynamics Laboratory, Utah State University, 4120 Old Main Hill, Logan, UT 84322-4120, USA
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Received: 7 February 2019 / Revised: 23 February 2019 / Accepted: 1 March 2019 / Published: 5 March 2019
(This article belongs to the Section Signal and Data Analysis)
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Abstract

We consider the sparse recovery problem of signals with an unknown clustering pattern in the context of multiple measurement vectors (MMVs) using the compressive sensing (CS) technique. For many MMVs in practice, the solution matrix exhibits some sort of clustered sparsity pattern, or clumpy behavior, along each column, as well as joint sparsity across the columns. In this paper, we propose a new sparse Bayesian learning (SBL) method that incorporates a total variation-like prior as a measure of the overall clustering pattern in the solution. We further incorporate a parameter in this prior to account for the emphasis on the amount of clumpiness in the supports of the solution to improve the recovery performance of sparse signals with an unknown clustering pattern. This parameter does not exist in the other existing algorithms and is learned via our hierarchical SBL algorithm. While the proposed algorithm is constructed for the MMVs, it can also be applied to the single measurement vector (SMV) problems. Simulation results show the effectiveness of our algorithm compared to other algorithms for both SMV and MMVs. View Full-Text
Keywords: compressed sensing (CS); sparse Bayesian learning (SBL); joint sparsity; cluster structured sparsity; single measurement vector (SMV); multiple measurement vectors (MMVs) compressed sensing (CS); sparse Bayesian learning (SBL); joint sparsity; cluster structured sparsity; single measurement vector (SMV); multiple measurement vectors (MMVs)
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Shekaramiz, M.; Moon, T.K.; Gunther, J.H. Bayesian Compressive Sensing of Sparse Signals with Unknown Clustering Patterns. Entropy 2019, 21, 247.

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