Compressive sensing (CS) is an emerging fi eld based on the revelation that a small collection of linear projections of a sparse signal contains enough information for sta- ble, 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 approximate Bayesian infer- ence using belief propagation (BP) decoding, which represents the CS encoding matrix as a graphical model. Fast encoding and decoding is provided using sparse encoding matrices, which also improve BP convergence by reducing the presence of loops in the graph. To decode a length-N signal containing K large coeffi cients, our CS-BP decoding algorithm uses O(K log(N)) measurements and O(N log2 (N)) computation. Finally, sparse encoding matrices and the CS-BP decoding algorithm can be modifi ed to support a variety of signal models and measurement noi

0812.4627v1[1].pdf

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