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压缩感知理论及其研究进展
引用本文:石光明,刘丹华,高大化,刘哲,林杰,王良君.压缩感知理论及其研究进展[J].电子学报,2009,37(5):1070-1081.
作者姓名:石光明  刘丹华  高大化  刘哲  林杰  王良君
作者单位: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. 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;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
基金项目:国家自然科学基金,教育部长江学者和创新团队支持计划,国家高技术研究发展计划(863计划) 
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
收稿时间:2008-07-02

Advances in Theory and Application of Compressed Sensing
SHI Guang-ming,LIU Dan-hua,GAO Da-hua,LIU Zhe,LIN Jie,WANG Liang-jun.Advances in Theory and Application of Compressed Sensing[J].Acta Electronica Sinica,2009,37(5):1070-1081.
Authors:SHI Guang-ming  LIU Dan-hua  GAO Da-hua  LIU Zhe  LIN Jie  WANG Liang-jun
Affiliation: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;Shaanxi 710051;3.School of Science;Northwestern Polytechnical University;Shaanxi 710072;China
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.
Keywords:information sampling  compressed sensing  sparse representation  measurement matrix  
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