Two-Channel Critically-Sampled Graph Filter Banks With Spectral Domain Sampling
arXiv:1804.08811 · doi:10.1109/TSP.2019.2892033
Abstract
We propose two-channel critically-sampled filter banks for signals on undirected graphs that utilize spectral domain sampling. Unlike conventional approaches based on vertex domain sampling, our transforms have the following desirable properties: 1) perfect reconstruction regardless of the characteristics of the underlying graphs and graph variation operators and 2) a symmetric structure; i.e., both analysis and synthesis filter banks are built using similar building blocks. Along with the structure of the filter banks, this paper also proves the general criterion for perfect reconstruction and theoretically shows that the vertex and spectral domain sampling coincide for a special case. The effectiveness of our approach is evaluated by comparing its performance in nonlinear approximation and denoising with various conventional graph transforms.
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Cited by in corpus (11)
- Sampling Signals on Graphs: From Theory to Applications
- Graph Unrolling Networks: Interpretable Neural Networks for Graph Signal Denoising
- Generalized Sampling on Graphs With Subspace and Smoothness Priors
- Graph Signal Sampling Under Stochastic Priors
- Two Channel Filter Banks on Arbitrary Graphs with Positive Semi Definite Variation Operators
- Graph Signal Processing: Modulation, Convolution, and Sampling
- M-Channel Critically Sampled Spectral Graph Filter Banks With Symmetric Structure
- Spectral Domain Spline Graph Filter Bank
- Polynomial graph filter of multiple shifts and distributed implementation of inverse filtering
- Sampling and Recovery of Graph Signals based on Graph Neural Networks
- Graph Blind Deconvolution with Sparseness Constraint