电子学报 ›› 2009, Vol. 37 ›› Issue (5): 1070-1081.

• 论文 • 上一篇    下一篇

压缩感知理论及其研究进展

石光明1, 刘丹华1, 高大化1,2, 刘 哲3, 林 杰1, 王良君1   

  1. 1. 西安电子科技大学智能感知与图像理解教育部重点实验室,陕西西安 710071;2. 空军工程大学理学院,陕西西安 710051;3. 西北工业大学理学院,陕西西安 710072
  • 收稿日期:2008-07-02 修回日期:2008-11-10 出版日期:2009-05-25 发布日期:2009-05-25

Advances in Theory and Application of Compressed Sensing

SHI Guang-ming1, LIU Dan-hua1, GAO Da-hua1,2, LIU Zhe3, LIN Jie1, WANG Liang-jun1   

  1. 1. Intelligent Perception and Image Understanding Key Laboratory of Ministry of Education,Xidian University,Xi’an,Shaanxi 710071,China;2. School of Science, Air Force Engineering University, Xi’an,Shaanxi 710051,China;3. School of Science, Northwestern Polytechnical University, Xi’an,Shaanxi 710072,China
  • Received:2008-07-02 Revised:2008-11-10 Online:2009-05-25 Published:2009-05-25

摘要: 信号采样是联系模拟信源和数字信息的桥梁.人们对信息的巨量需求造成了信号采样、传输和存储的巨大压力.如何缓解这种压力又能有效提取承载在信号中的有用信息是信号与信息处理中急需解决的问题之一.近年国际上出现的压缩感知理论(Compressed Sensing,CS)为缓解这些压力提供了解决方法.本文综述了CS理论框架及关键技术问题,并着重介绍了信号稀疏变换、观测矩阵设计和重构算法三个方面的最新进展,评述了其中的公开问题,对研究中现存的难点问题进行了探讨,最后介绍了CS理论的应用领域.

关键词: 信息采样, 压缩感知, 稀疏表示, 观测矩阵

Abstract: Sampling is the bridge between analog source signal and digital signal.With the rapid progress of information technologies,the demands for information are increasing dramatically.So the existing systems are very difficult to meet the challenges of high speed sampling,large volume data transmission and storage.How to acquire information in signal efficiently is an urgent problem in electronic information fields.In recent years,an emerging theory of signal acquirement——compressed sensing (CS) provides a golden opportunity for solving this problem.This paper reviews the theoretical framework and the key technical problems of compressed sensing and introduces the latest developments of signal sparse representation,design of measurement matrix and reconstruction algorithm.Then this paper also reviews several open problems in CS theory and discusses the existing difficult problems.In the end,the application fields of compressed sensing are introduced.

Key words: information sampling, compressed sensing, sparse representation, measurement matrix

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