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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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 61; no. 2; pp. 340 - 354
Main Authors: Ziniel, J., Schniter, P.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.01.2013
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Description
Summary: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.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2012.2222382