Description: 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
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