A Hilbert Space Theory of Generalized Graph Signal Processing
arXiv:1904.11655 · doi:10.1109/TSP.2019.2952055
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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Cited by in corpus (12)
- Multi-way Graph Signal Processing on Tensors: Integrative analysis of irregular geometries
- Time-varying Signals Recovery via Graph Neural Networks
- Sampling Theory of Jointly Bandlimited Time-vertex Graph Signals
- Wide-Sense Stationarity in Generalized Graph Signal Processing
- Signal processing on simplicial complexes
- 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