压缩感知的信息论解译
发布时间：2018-10-08 09:26
【摘要】：压缩感知(compressed sensing or compressive sampling,CS)是数据采集与信号重构的新体制,其与信息论的关系是,应该且可以从信息论的角度对CS进行分析,而CS丰富和发展着信息论的内涵和外延。换言之,信息论的一些基本概念和原理(如信源、信道、信源编码、信道编码、率失真、Fano不等式、数据处理定理等)为CS研究提供了理论基础,尤其是在性能限(如采样数)的界定等方面;另一方面,CS提供了采集、存贮、传输、恢复稀疏信号的高效方法,以其独特的理念和算法模式,提供了直接对信息的采样和处理机制,延拓了经典信息论的范畴。本文将梳理和阐释CS和信息论之间的关系,力图从信息论角度揭示CS中的一些基本问题,尤其是CS采样问题,并寻求用信息论指导CS的学习与研究。
[Abstract]:Compressed perceptual (compressed sensing or compressive sampling,CS (compressed sensing or compressive sampling,CS) is a new system of data acquisition and signal reconstruction. Its relationship with information theory is that CS should and can be analyzed from the angle of information theory, and CS enriches and develops the connotation and extension of information theory. In other words, some basic concepts and principles of information theory (such as source, channel, source coding, channel coding, rate-distortion Fano inequality, data processing theorem, etc.) provide a theoretical basis for the study of CS. On the other hand, CS provides an efficient method of collecting, storing, transmitting and restoring sparse signal, with its unique idea and algorithm mode. The mechanism of direct sampling and processing of information is provided, and the category of classical information theory is extended. This paper will comb and explain the relationship between CS and information theory, try to reveal some basic problems in CS from the angle of information theory, especially the problem of CS sampling, and seek to use information theory to guide the study and research of CS.
【作者单位】： 武汉大学遥感信息工程学院;武汉纺织大学电子与电气工程学院;
【基金】：国家973计划资助项目(2010CB731905) 国家自然科学基金资助项目(41071286) 湖北省教育厅基金资助项目(D201416022)~~
【分类号】：TN911.7
，
本文编号：2256268
[Abstract]:Compressed perceptual (compressed sensing or compressive sampling,CS (compressed sensing or compressive sampling,CS) is a new system of data acquisition and signal reconstruction. Its relationship with information theory is that CS should and can be analyzed from the angle of information theory, and CS enriches and develops the connotation and extension of information theory. In other words, some basic concepts and principles of information theory (such as source, channel, source coding, channel coding, rate-distortion Fano inequality, data processing theorem, etc.) provide a theoretical basis for the study of CS. On the other hand, CS provides an efficient method of collecting, storing, transmitting and restoring sparse signal, with its unique idea and algorithm mode. The mechanism of direct sampling and processing of information is provided, and the category of classical information theory is extended. This paper will comb and explain the relationship between CS and information theory, try to reveal some basic problems in CS from the angle of information theory, especially the problem of CS sampling, and seek to use information theory to guide the study and research of CS.
【作者单位】： 武汉大学遥感信息工程学院;武汉纺织大学电子与电气工程学院;
【基金】：国家973计划资助项目(2010CB731905) 国家自然科学基金资助项目(41071286) 湖北省教育厅基金资助项目(D201416022)~~
【分类号】：TN911.7
，
本文编号：2256268
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