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Efficient highdimensional inference in the multiple measurement vector problem.” arXiv:1111.5272 [cs.IT
, 2011
"... Abstract—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 alg ..."
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Cited by 5 (4 self)
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Abstract—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, AMPMMV, is capable of exploiting temporal correlations in the amplitudes of nonzero 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 amplitudecorrelated MMV setting. Aided by these techniques, AMPMMV offers a computational complexity that is linear in all problem dimensions. In order to allow for automatic parameter tuning, an expectationmaximization algorithm that complements AMPMMV is described. Finally, a detailed numerical study demonstrates the power of the proposed approach and its particular suitability for application to highdimensional problems. Index Terms—Approximate message passing (AMP), belief propagation, compressed sensing, expectationmaximization algorithms, joint sparsity, Kalman filters, multiple measurement vector problem, statistical signal processing. I.
Message passing approaches to compressive inference under structured signal priors
, 2013
"... Across numerous disciplines, the ability to generate highdimensional datasets is driving an enormous demand for increasingly efficient ways of both capturing and processing this data. A promising recent trend for addressing these needs has developed from the recognition that, despite living in hi ..."
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Cited by 2 (2 self)
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Across numerous disciplines, the ability to generate highdimensional datasets is driving an enormous demand for increasingly efficient ways of both capturing and processing this data. A promising recent trend for addressing these needs has developed from the recognition that, despite living in highdimensional ambient spaces, many datasets have vastly smaller intrinsic dimensionality. When capturing (sampling) such datasets, exploiting this realization permits one to dramatically reduce the number of samples that must be acquired without losing the salient features of the data. When processing such datasets, the reduced intrinsic dimensionality can be leveraged to allow reliable inferences to be made in scenarios where it is infeasible to collect the amount of data that would be required for inference using classical techniques. To date, most approaches for taking advantage of the low intrinsic dimensionality inherent in many datasets have focused on identifying succinct (i.e., sparse) representations of the data, seeking to represent the data using only a handful of “significant ” elements from an appropriately chosen dictionary. While powerful in
Efficient Message PassingBased Inference in the Multiple Measurement Vector Problem
"... Abstract—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 alg ..."
Abstract

Cited by 1 (1 self)
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Abstract—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, AMPMMV, is capable of exploiting temporal correlations in the amplitudes of nonzero 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 (AMP) techniques to the amplitudecorrelated MMV setting. Aided by these techniques, AMPMMV offers a computational complexity that is linear in all problem dimensions. In order to allow for automatic parameter tuning, an expectationmaximization algorithm that complements AMPMMV is described. Finally, a numerical study demonstrates the power of the proposed approach and its particular suitability for application to highdimensional problems. I.
Efficient HighDimensional Inference in the 1 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 ..."
Abstract
 Add to MetaCart
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, AMPMMV, is capable of exploiting temporal correlations in the amplitudes of nonzero 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 amplitudecorrelated MMV setting. Aided by these techniques, AMPMMV offers a computational complexity that is linear in all problem dimensions. In order to allow for automatic parameter tuning, an expectationmaximization algorithm that complements AMPMMV is described. Finally, a detailed numerical study demonstrates the power of the proposed approach and its particular suitability for application to highdimensional problems. I.