经典的香农采样定理认为,为了不失真地恢复模拟信号,采样频率应该不小于奈奎斯特频率(即模拟信号

频谱中的最高频率)的两倍.但是其中除了利用到信号是有限带宽的假设外,没利用任何的其它先验信息.采集到

的数据存在很大程度的冗余.Donoho等人提出的压缩感知方法(Compressed Sensing或Compressive Sampling,

CS)充分运用了大部分信号在预知的一组基上可以稀疏表示这一先验信息,利用随机投影实现了在远低于奈奎斯

特频率的采样频率下对压缩数据的直接采集.该方法不仅为降低采样频率提供了一种新思路,也为其它科学领域

的研究提供了新的契机.该文综述性地阐述了压缩感知方法的基本原理,给出了其中的一些约束问题和估计方法,

并介绍压缩感知理论的相关问题———矩阵填充,最后讨论了其未来可能的应用前景.

-According to the conventional Shannon s sampling theorem,in order to represent the

analog signal,the sampling rate should not be less than twice the Nyquist sampling rate.Howev-

er,this theorem only makes use of the bandwidth information.As a result,the collected data

contain many redundant information.The recently proposed sampling method,compressed sens-

ing or compressive sampling(CS),can collect compressed data at the sampling rate much lower

than that needed in Shannon s sampling theorem by exploring the compressibility of the signal.

This paper presents a review on the basic theory of CS.Some of the restrictions and recovery

methods in CS are also discussed.Finally,some potential applications based on CS are presented.