电子学报 ›› 2011, Vol. 39 ›› Issue (7): 1651-1662.

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压缩感知回顾与展望

焦李成, 杨淑媛, 刘芳, 侯彪   

  1. 智能感知与图像理解教育部重点实验室,西安电子科技大学,陕西西安 710071
  • 收稿日期:2011-05-20 修回日期:2011-06-06 出版日期:2011-07-25 发布日期:2011-07-25

Development and Prospect of Compressive Sensing

JIAO Li-cheng, YANG Shu-yuan, LIU Fang, HOU Biao   

  1. Key Lab of Intelligent Perception and Image Understanding of Ministry of Education,Xidian University,Xi'an,Shaanxi 710071,China
  • Received:2011-05-20 Revised:2011-06-06 Online:2011-07-25 Published:2011-07-25

摘要:

压缩感知是建立在矩阵分析、统计概率论、拓扑几何、优化与运筹学、泛函分析等基础上的一种全新的信息获取与处理的理论框架.它基于信号的可压缩性,通过低维空间、低分辨率、欠Nyquist采样数据的非相关观测来实现高维信号的感知.压缩感知不仅让我们重新审视线性问题,而且丰富了关于信号恢复的优化策略,极大的促进了数学理论和工程应用的结合.目前,压缩感知的研究正从早期的概念理解、数值仿真、原理验证、系统初步设计等阶段,转入到理论的进一步深化,以及实际系统的开发与应用阶段.本文分析了压缩感知的原理与应用,综述了压缩感知的最新进展及存在的问题,指出了进一步研究的方向.

关键词: 压缩感知, 稀疏表示, 压缩观测, 优化恢复

Abstract:

Compressive Sensing(CS) is a new developed theoretical framework for information acquisition and processing,which is based on matrix analysis,statistical probability theory,topological geometry,optimization and opsearch,functional analysis and so on.The high-dimensional signals can be recovered from the low-dimensional and sub-Nyquist sampling data based on the compressibility of signals.It not only inspires us to survey the linear problem again,but also enriches the optimization approaches for signal recovery to promote the combination of mathematics with engineering application.Nowadays the researches on compressive sensing have developed from the earlier concept understanding,numerical simulation,principle verification,and primary system designation,to the deeper researches on theory,development and application of practical system.In this paper,we introduce the basic idea of compressive sensing,and the development history,current and future challenges.

Key words: compressive sensing, sparse representation, compressive measurement, optimization recovery

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