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arXiv · 1904.11655

A Hilbert Space Theory of Generalized Graph Signal Processing

Feng Ji·Wee Peng Tay
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Abstract

Graph signal processing (GSP) has become an important tool in many areas such as image processing, networking learning and analysis of social network data. In this paper, we propose a broader framework that not only encompasses traditional GSP as a special case, but also includes a hybrid framework of graph and classical signal processing over a continuous domain. Our framework relies extensively on concepts and tools from functional analysis to generalize traditional GSP to graph signals in a separable Hilbert space with infinite dimensions. We develop a concept analogous to Fourier transform for generalized GSP and the theory of filtering and sampling such signals.

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BibTeXRIS

Feng Ji, Wee Peng Tay. 2019-04-26. A Hilbert Space Theory of Generalized Graph Signal Processing. https://doi.org/10.1109/tsp.2019.2952055

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