A Hilbert space theory of generalized graph signal processing

• Main Authors: Ji, Feng, Tay, Wee Peng
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2021
• Subjects: Engineering::Electrical and electronic engineering; Graph Signal Proceesing; Hilbert Space
• Online Access: https://hdl.handle.net/10356/154495
• Institution: Nanyang Technological University

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.