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Entropy 2019, 21(4), 332; https://doi.org/10.3390/e21040332

Isometric Signal Processing under Information Geometric Framework

College of Electronic Science, National University of Defense Technology, Changsha 410073, China
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Received: 28 February 2019 / Revised: 20 March 2019 / Accepted: 25 March 2019 / Published: 27 March 2019
(This article belongs to the Section Information Theory, Probability and Statistics)
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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. View Full-Text
Keywords: information geometry; intrinsic parameter submanifold; isometric signal processing information geometry; intrinsic parameter submanifold; isometric signal processing
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Wu, H.; Cheng, Y.; Wang, H. Isometric Signal Processing under Information Geometric Framework. Entropy 2019, 21, 332.

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