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。
Discriminant space defining area classes is an important conceptual construct for uncertainty characterization in area-class maps.Discriminant models were promoted as they can enhance consistency in area-class mapping and replicability in error modeling.As area classes are rarely completely separable in empirically realized discriminant space,where class inseparabil-ity becomes more complicated for change categorization,we seek to quantify uncertainty in area classes(and change classes)due to measurement errors and semantic discrepancy separately and hence assess their relative margins objectively.Experiments using real datasets were carried out,and a Bayesian method was used to obtain change maps.We found that there are large differences be-tween uncertainty statistics referring to data classes and information classes.Therefore,uncertainty characterization in change categorization should be based on discriminant modeling of measurement errors and semantic mismatch analysis,enabling quanti-fication of uncertainty due to partially random measurement errors,and systematic categorical discrepancies,respectively.
