Bayesian Compressive Sensing Via Belief Propagation

作者：Dror Baron, Shriram Sarvotham, Richard G. Baraniuk · 发表于：IEEE Transactions on Signal Processing · 年份：2009 · DOI：10.1109/tsp.2009.2027773 · 被引用次数：515 · 研究领域：Sparse and Compressive Sensing Techniques、Blind Source Separation Techniques、Distributed Sensor Networks and Detection Algorithms

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 containingKlarge coefficients, our CS-BP decoding algorithm uses O(K log(N)) measurements and O(N log2(N)) computation. Finally, although we focus on a two-state mixture Gaussian model, CS-BP is easily adapted to other signal models.