Efficient High-Dimensional Inference in the Multiple Measurement Vector Problem

In this work, a Bayesian approximate message passing algorithm is proposed for solving the multiple measurement vector (MMV) problem in compressive sensing, in which a collection of sparse signal vectors that share a common support are recovered from undersampled noisy measurements. The algorithm, A...

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Vydáno v:	IEEE transactions on signal processing Ročník 61; číslo 2; s. 340 - 354
Hlavní autoři:	Ziniel, J., Schniter, P.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.01.2013 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Algorithms Applied sciences Approximate message passing (AMP) Approximation Approximation algorithms Bayesian methods belief propagation Complexity theory compressed sensing Correlation Detection, estimation, filtering, equalization, prediction Exact sciences and technology expectation-maximization algorithms Inference Information, signal and communications theory joint sparsity Joints Kalman filters Mathematical analysis Mathematical models Message passing multiple measurement vector problem Noise measurement Sampling, quantization Signal and communications theory Signal, noise statistical signal processing Studies Telecommunications and information theory Tuning Vectors Vectors (mathematics) joint sparsity statistical signal processing belief propagation expectation-maximization algorithms Kalman filter Signal estimation Time correlation Computational complexity Approximate message passing (AMP) Credal approach Message passing Signal processing multiple measurement vector problem Automatic tuning Kalman filters EM algorithm Compressed sensing
ISSN:	1053-587X, 1941-0476
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Popis
Shrnutí:	In this work, a Bayesian approximate message passing algorithm is proposed for solving the multiple measurement vector (MMV) problem in compressive sensing, in which a collection of sparse signal vectors that share a common support are recovered from undersampled noisy measurements. The algorithm, AMP-MMV, is capable of exploiting temporal correlations in the amplitudes of non-zero coefficients, and provides soft estimates of the signal vectors as well as the underlying support. Central to the proposed approach is an extension of recently developed approximate message passing techniques to the amplitude-correlated MMV setting. Aided by these techniques, AMP-MMV offers a computational complexity that is linear in all problem dimensions. In order to allow for automatic parameter tuning, an expectation-maximization algorithm that complements AMP-MMV is described. Finally, a detailed numerical study demonstrates the power of the proposed approach and its particular suitability for application to high-dimensional problems.
Bibliografie:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 content type line 23
ISSN:	1053-587X 1941-0476
DOI:	10.1109/TSP.2012.2222382