Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 58, Issue 1, Pages 269-280Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2009.2027773
Keywords
Bayesian inference; belief propagation; compressive sensing; fast algorithms; sparse matrices
Categories
Funding
- NSF [CCF-0431150, CCF-0728867]
- DARPA/ONR [N66001-08-1-2065]
- ONR [N00014-07-1-0936, N00014-08-1-1112]
- AFOSR [FA9550-07-1-0301]
- ARO MURI [W311NF-07-1-0185]
- Texas Instruments Leadership University
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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.
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