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A graph signal processing toolbox built on pytorch. The repository now mainly consists of the following stuffs:

1. GFT-based filter(banks) processing multi-dimensional signals in a Multiple Input Multiple Output(MIMO) manner.
2. GraphQmf and GraphBiorth wavelet filter bank.
3. Many strategies to decompose an arbitrary graph into many(usually <10) bipartite graphs.
4. Many graph signal sampling(which differs slightly with general graph sampling) and reconstruction algorithms.

As this package is built on PyTorch and pytorch_sparse, you can easily integrate functionalities from thgsp into a PyTorch pipeline. Check the document for installation and introduction.

Table of Contents

• Example
• Reference
• Citation

Example

GraphQMF four channel wavelet filter bank on Minnesota

The Minnesota traffic network is 3-colorable(exactly) or 4-colorable(roughly). Hence 4-channel GraphQmf filterbank is constructed, requiring a ceil(log2(4))=2 level bipartite decomposition. The bipartite graphs are below.

The comparision between the eventual reconstructed signal and the input one.

GraphBiorth four channel wavelet filter bank for camera man.

See the full program here.

Reference

[David K Hammond, et al.] Wavelets on Graphs via Spectral Graph Theory
[Sunil K. Narang, et al.] Compact Support Biorthogonal Wavelet Filterbanks for Arbitrary Undirected Graphs
[Sunil K. Narang, et al.] Perfect Reconstruction Two-Channel Wavelet Filter Banks for Graph Structured Data
[Akie Sakiyama, et al.] Oversampled Graph Laplacian Matrix for Graph Filter Banks
[Jing Zen, et al.] Bipartite Subgraph Decomposition for Critically Sampledwavelet Filterbanks on Arbitrary Graphs
[Aamir Anis, et al.] Towards a Sampling Theorem for Signals on Arbitrary Graphs
[Aimin Jiang, et al.] Admm-based Bipartite Graph Approximation
[Yuanchao Bai, et al.] Fast graph sampling set selection using Gershgorin disc alignment, IEEE TSP, 2020
[G. Puy, et al.] Random sampling of bandlimited signals on graphs, ACHA, 2018.
[A. Sakiyama, et al.] Eigendecomposition-free sampling set selection for graph signals，IEEE TSP, 2020.
[Aamir Anis et al.] Efficient sampling set selection for bandlimited graph signals using graph spectral proxies, IEEE TSP, 2016.

Citation

@misc{thgsp,
  author = {Bowen Deng},
  title = {ThGSP: A PyTorch-based Graph Signal Processing Library},
  year = {2021},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/bwdeng20/thgsp}},
}