论文部分内容阅读
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。
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 be analyzed from the perspective of information theory. CS enriches and develops the connotation of information theory And extension. 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 the theoretical basis for CS research, especially in the performance limits On the other hand, CS provides an efficient method of collecting, storing, transmitting and recovering sparse signals. With its unique concept and algorithm model, CS provides a direct sampling and processing mechanism for information, The category of classical information theory. This paper will sort out and explain the relationship between CS and information theory, trying to reveal some basic issues in CS from the perspective of information theory, especially the CS sampling problem, and seek to guide CS learning and research with information theory.