[1]沈益,朱歌.压缩感知理论综述与展望[J].西华师范大学学报(自然科学版),2018,39(04):337-344.[doi:10.16246/j.issn.1673-5072.2018.04.001]
 SHEN Yi,ZHU Ge.An Overview of Compressed Sensing Theory and Its Prospect[J].Journal of China West Normal University(Natural Sciences),2018,39(04):337-344.[doi:10.16246/j.issn.1673-5072.2018.04.001]
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压缩感知理论综述与展望

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《西华师范大学学报(自然科学版)》[ISSN:1673-5072/CN:51-1699/N]

卷:
39
期数:
2018年04期
页码:
337-344
栏目:
出版日期:
2018-12-20

文章信息/Info

Title:

An Overview of Compressed Sensing Theory and Its Prospect

作者:

沈益朱歌

(浙江理工大学 理学院,杭州  310018)

Author(s):

SHEN YiZHU Ge

Department of Mathematics,Zhejiang Sci-Tech University,Hangzhou 310018,China

关键词:

磁共振成像仪压缩感知稀疏信号等距约束性质正交匹配算法

Keywords:

magnetic resonance imagecompressed sensingsparse signalresisted isometry propertyorthogonal matching pursuit

分类号:
TN911;72
DOI:
10.16246/j.issn.1673-5072.2018.04.001
文献标志码:
A
摘要:

与传统压缩相比,压缩感知理论可由远低于Nyquist采样定理要求的采样点恢复信号。其基本思想是,对于稀疏或可压缩信号,用满足一定条件的观测矩阵将高维信号投影到低维空间,然后通过求解一个优化问题可高概率地恢复信号。该理论是目前应用数学领域的一个热门研究方向,一经提出,就被应用到核磁共振成像、遥感成像、单像素相机等领域。本文将综述压缩感知的一些基本知识,主要包括有限等距性质,紧小波框架下信号的稳定恢复以及正交匹配算法。

Abstract:

In comparison with the traditional compression,compressed sensing can recover the original signal with much less data than that of Nyquist sampling theorem.The basic idea is that,for sparse or compressible signals,high dimensional signals can be projected into low-dimensional space by using observation matrices that satisfies certain conditions,and then the signals can be high probability recovered by solving an optimization problem.The theorem is a popular research direction in the filed of applied mathematical.Once proposed,it is applied to the fields of medical MRI,remote sensing,single pixel camera and so on.In this paper,some basic results of compressed sensing are reviewed,including resisted isometry property,signal stable recovery of tight wavelet frame and orthogonal matching pursuit.

备注/Memo

备注/Memo:

收稿日期:2018-06-13
基金项目:国家自然科学基金项目(11671358)
作者简介:沈益(1982—),男,浙江台州人,博士,教授,主要从事小波分析与压缩感知研究。
通信作者:沈益,E-mail:yshen@zstu.edu.cn

更新日期/Last Update: 2018-12-20