信息几何框架下的等距信号处理

Isometric Signal Processing under Information Geometric Framework.

作者信息

Wu Hao, Cheng Yongqiang, Wang Hongqiang

机构信息

College of Electronic Science, National University of Defense Technology, Changsha 410073, China.

出版信息

Entropy (Basel). 2019 Mar 27;21(4):332. doi: 10.3390/e21040332.

DOI:10.3390/e21040332

PMID:33267047

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7514816/

Abstract

Information geometry is the study of the intrinsic geometric properties of manifolds consisting of a probability distribution and provides a deeper understanding of statistical inference. Based on this discipline, this letter reports on the influence of the signal processing on the geometric structure of the statistical manifold in terms of estimation issues. This letter defines the intrinsic parameter submanifold, which reflects the essential geometric characteristics of the estimation issues. Moreover, the intrinsic parameter submanifold is proven to be a tighter one after signal processing. In addition, the necessary and sufficient condition of invariant signal processing of the geometric structure, i.e., isometric signal processing, is given. Specifically, considering the processing with the linear form, the construction method of linear isometric signal processing is proposed, and its properties are presented in this letter.

摘要

信息几何是对由概率分布构成的流形的内在几何性质的研究，并能更深入地理解统计推断。基于这一学科，本文从估计问题的角度报告了信号处理对统计流形几何结构的影响。本文定义了内在参数子流形，它反映了估计问题的本质几何特征。此外，经证明，信号处理后的内在参数子流形更为紧致。另外，还给出了几何结构不变信号处理（即等距信号处理）的充要条件。具体而言，考虑线性形式的处理，本文提出了线性等距信号处理的构造方法，并阐述了其性质。