Subgraph-based filterbanks for graph signals

Abstract

We design a critically-sampled compact-support biorthogonal transform for graph signals, via graph filterbanks. Instead of partitioning the nodes in two sets so as to remove one every two nodes in the filterbank downsampling operations, the design is based on a partition of the graph in connected subgraphs. Coarsening is achieved by defining one "supernode" for each subgraph and the edges for this coarsened graph derives from the connectivity between the subgraphs. Unlike the "one every two nodes" downsampling on bipartite graphs, this coarsening operation does not have an exact formulation in the graph Fourier domain. Instead, we rely on the local Fourier bases of each subgraph to define filtering operations. We apply successfully this method to decompose graph signals, and show promising performance on compression and denoising.

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Cited by in corpus (13)

• Graph Unrolling Networks: Interpretable Neural Networks for Graph Signal Denoising
• Spectral Domain Sampling of Graph Signals
• Deep Unsupervised Learning of 3D Point Clouds via Graph Topology Inference and Filtering
• Two-Channel Critically-Sampled Graph Filter Banks With Spectral Domain Sampling
• Learning Graphs with Monotone Topology Properties and Multiple Connected Components
• Generalized Sampling on Graphs With Subspace and Smoothness Priors
• Graph Fourier Transform Based on ${\ell }_1$ Norm Variation Minimization
• Graph Signal Processing -- Part II: Processing and Analyzing Signals on Graphs
• Graph Convolutional Networks with EigenPooling
• Spectral Domain Spline Graph Filter Bank
• Graph spectral characterisation of the XY model on complex networks
• Multiscale Graph Construction Using Non-local Cluster Features
• Joint Forecasting and Interpolation of Graph Signals Using Deep Learning