压缩传感是一个从2006年左右开始兴起的研究领域，它关注于如何采样信号，也就是信号的采样方式或者压缩方式。通过设计一种特殊的采样方案，可以使得采样频率降低为信号的“信息率”，而不是传统的奈奎斯特采样率，于是，实际的采样率可以大大低于奈奎斯特频率，却只损失很少的信息量，依然保持了充足的信息量足以恢复出采样前的原始信号。这个研究思想挑战了奈奎斯特频率的理论极限，会对整个信号处理领域产生极其深远的影响，同时，信号处理的许多应用领域也会随之发生根本性的发展和变化。

-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