Belief propagation for joint sparse recovery

Abstract

Compressed sensing (CS) demonstrates that sparse signals can be recovered from underdetermined linear measurements. We focus on the joint sparse recovery problem where multiple signals share the same common sparse support sets, and they are measured through the same sensing matrix. Leveraging a recent information theoretic characterization of single signal CS, we formulate the optimal minimum mean square error (MMSE) estimation problem, and derive a belief propagation algorithm, its relaxed version, for the joint sparse recovery problem and an approximate message passing algorithm. In addition, using density evolution, we provide a sufficient condition for exact recovery.

8 pages, 2 figures

References in corpus (3)

• Message Passing Algorithms for Compressed Sensing
• Asymptotic Analysis of MAP Estimation via the Replica Method and Applications to Compressed Sensing
• Compressive MUSIC: A Missing Link Between Compressive Sensing and Array Signal Processing

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