A Hilbert Space Theory of Generalized Graph Signal Processing

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.

References in corpus (3)

• Semi-Supervised Classification with Graph Convolutional Networks
• Discrete Signal Processing on Graphs
• Advances in Distributed Graph Filtering

Cited by in corpus (12)

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• Subset Random Sampling and Reconstruction of Finite Time-Vertex Graph Signals
• Folded Graph Signals: Sensing with Unlimited Dynamic Range
• GFCN: A New Graph Convolutional Network Based on Parallel Flows
• Graph Signal Processing over a Probability Space of Shift Operators
• Subgraph Signal Processing
• Sampling Theory of Bandlimited Continuous-Time Graph Signals
• Signal processing with a distribution of graph operators