摘要
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. However, 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 sensing 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.
出处
《计算机学报》
EI
CSCD
北大核心
2011年第3期425-434,共10页
Chinese Journal of Computers
基金
国家"九七三"重点基础研究发展规划项目基金(2010CB731800)
国家自然科学重点基金(60933006)与面上基金(60972013)资助~~
关键词
压缩感知
贪婪算法
线性规划
随机投影
compressed sensing
greedy algorithms
linear programming
random projection
