Expectation-Maximization Gaussian-Mixture Approximate Message Passing

When recovering a sparse signal from noisy compressive linear measurements, the distribution of the signal's non-zero coefficients can have a profound effect on recovery mean-squared error (MSE). If this distribution was a priori known, then one could use computationally efficient approximate m...

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Vydané v:	IEEE transactions on signal processing Ročník 61; číslo 19; s. 4658 - 4672
Hlavní autori:	Vila, Jeremy P., Schniter, Philip
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York, NY IEEE 01.10.2013 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	Algorithms Applied sciences Approximation Approximation algorithms belief propagation Complexity theory Compressed sensing Detection, estimation, filtering, equalization, prediction Exact sciences and technology expectation maximization algorithms Gaussian mixture model Information, signal and communications theory Mathematical models Maximization Message passing Noise Noise measurement Reconstruction Recovery Run time (computers) Sampling, quantization Sensors Signal and communications theory Signal, noise Telecommunications and information theory Vectors Performance evaluation State of the art belief propagation Mixture theory Implementation Gaussian mixture model Mean square error Credal approach Gaussian process Message passing Minimax method A priori estimation Signal processing expectation maximization algorithms Bayes methods EM algorithm Compressed sensing
ISSN:	1053-587X, 1941-0476
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Popis
Shrnutí:	When recovering a sparse signal from noisy compressive linear measurements, the distribution of the signal's non-zero coefficients can have a profound effect on recovery mean-squared error (MSE). If this distribution was a priori known, then one could use computationally efficient approximate message passing (AMP) techniques for nearly minimum MSE (MMSE) recovery. In practice, however, the distribution is unknown, motivating the use of robust algorithms like LASSO-which is nearly minimax optimal-at the cost of significantly larger MSE for non-least-favorable distributions. As an alternative, we propose an empirical-Bayesian technique that simultaneously learns the signal distribution while MMSE-recovering the signal-according to the learned distribution-using AMP. In particular, we model the non-zero distribution as a Gaussian mixture and learn its parameters through expectation maximization, using AMP to implement the expectation step. Numerical experiments on a wide range of signal classes confirm the state-of-the-art performance of our approach, in both reconstruction error and runtime, in the high-dimensional regime, for most (but not all) sensing operators.
Bibliografia:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 content type line 23 ObjectType-Article-1 ObjectType-Feature-2
ISSN:	1053-587X 1941-0476
DOI:	10.1109/TSP.2013.2272287