Bayesian Compressive Sensing Via Belief Propagation

Compressive sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable, sub-Nyquist signal acquisition. When a statistical characterization of the signal is available, Bayesian inference can comple...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2010-01, Vol.58 (1), p.269-280
Main Authors: Baron, D., Sarvotham, S., Baraniuk, R.G.
Format: Article
Language:English
Subjects:
Applied sciences
Bayesian inference
Bayesian methods
Belief propagation
Coding, codes
compressive sensing
Decoding
Detection, estimation, filtering, equalization, prediction
Encoding
Exact sciences and technology
fast algorithms
Graphical models
Greedy algorithms
Inference algorithms
Information, signal and communications theory
Length measurement
Linear programming
Miscellaneous
Signal and communications theory
Signal processing
Signal, noise
Sparse matrices
Telecommunications and information theory
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Description
Summary:Compressive sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable, sub-Nyquist signal acquisition. When a statistical characterization of the signal is available, Bayesian inference can complement conventional CS methods based on linear programming or greedy algorithms. We perform asymptotically optimal Bayesian inference using belief propagation (BP) decoding, which represents the CS encoding matrix as a graphical model. Fast computation is obtained by reducing the size of the graphical model with sparse encoding matrices. To decode a length-N signal containing K large coefficients, our CS-BP decoding algorithm uses O(K log(N)) measurements and O(N log 2 (N)) computation. Finally, although we focus on a two-state mixture Gaussian model, CS-BP is easily adapted to other signal models.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2009.2027773