https://github.com/ucd4ids/multiscalegraphsignaltransforms.jl

MultiscaleGraphSignalTransforms.jl is a collection of software tools written in the Julia programming language for graph signal processing including HGLET, GHWT, eGHWT, NGWP, Lapped NGWP, and Lapped HGLET. Some of them were originally written in MATLAB by Jeff Irion, but we added more functionalities, e.g., eGHWT, NGWP, etc.
https://github.com/ucd4ids/multiscalegraphsignaltransforms.jl

adapted-time-frequency-analysis eghwt ghwt graph-laplacian graph-signal-processing hglet lapped-orthogonal-transform multiscale-basis-dictionaries ngwp spectral-clustering the-best-basis-algorithm wavelets-on-graphs

Last synced: 8 months ago
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MultiscaleGraphSignalTransforms.jl is a collection of software tools written in the Julia programming language for graph signal processing including HGLET, GHWT, eGHWT, NGWP, Lapped NGWP, and Lapped HGLET. Some of them were originally written in MATLAB by Jeff Irion, but we added more functionalities, e.g., eGHWT, NGWP, etc.

• Host: GitHub
• URL: https://github.com/ucd4ids/multiscalegraphsignaltransforms.jl
• Owner: UCD4IDS
• License: other
• Created: 2021-04-21T21:13:57.000Z (about 5 years ago)
• Default Branch: master
• Last Pushed: 2025-09-09T22:03:34.000Z (9 months ago)
• Last Synced: 2025-09-09T22:28:43.821Z (9 months ago)
• Topics: adapted-time-frequency-analysis, eghwt, ghwt, graph-laplacian, graph-signal-processing, hglet, lapped-orthogonal-transform, multiscale-basis-dictionaries, ngwp, spectral-clustering, the-best-basis-algorithm, wavelets-on-graphs
• Language: Julia
• Homepage:
• Size: 116 MB
• Stars: 10
• Watchers: 1
• Forks: 3
• Open Issues: 1
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

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README

          
# MultiscaleGraphSignalTransforms.jl

| Doc | Build | Test |

|------|-------|------|

| [![](https://img.shields.io/badge/docs-passing-success)](https://ucd4ids.github.io/MultiscaleGraphSignalTransforms.jl/dev/) | [![CI](https://github.com/UCD4IDS/MultiscaleGraphSignalTransforms.jl/actions/workflows/CI.yml/badge.svg)](https://github.com/UCD4IDS/MultiscaleGraphSignalTransforms.jl/actions) | [![codecov](https://codecov.io/gh/UCD4IDS/MultiscaleGraphSignalTransforms.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/UCD4IDS/MultiscaleGraphSignalTransforms.jl) |

![Haar-Walsh on R vs on Graph](./GHWT.png "Haar-Walsh on R vs on Graph")

## COPYRIGHT

Copyright 2015-2022 The Regents of the University of California

Implemented by Jeff Irion, Haotian Li, Naoki Saito, and Yiqun Shao

## SETUP

To install the MultiscaleGraphSignalTransforms.jl, run

```julia

julia> import Pkg; Pkg.add("MultiscaleGraphSignalTransforms")

julia> using MultiscaleGraphSignalTransforms

```

## GETTING STARTED

Currently, you can run a set of very small tests via ```] test MultiscaleGraphSignalTransforms```; see the actual file ```test/runtest.jl``` as well as [the documentation](https://ucd4ids.github.io/MultiscaleGraphSignalTransforms.jl/dev) for further information.

## REFERENCES

1. J. Irion and N. Saito, [Hierarchical graph Laplacian eigen transforms](https://www.math.ucdavis.edu/~saito/publications/hglets.html), *Japan SIAM Letters*, vol. 6, pp. 21-24, 2014.

2. J. Irion and N. Saito, [The generalized Haar-Walsh transform](https://www.math.ucdavis.edu/~saito/publications/ghwt.html), *Proc. 2014 IEEE Statistical Signal Processing Workshop*, pp. 488-491, 2014.

3. J. Irion and N. Saito, [Applied and computational harmonic analysis on

graphs and networks](https://www.math.ucdavis.edu/~saito/publications/spie15.html), *Wavelets and Sparsity XVI*, (M. Papadakis, V. K. Goyal, D. Van De Ville, eds.), *Proc. SPIE 9597*, Paper #95971F, Invited paper, 2015.

4. J. Irion, [Multiscale Transforms for Signals on Graphs: Methods and Applications](https://jefflirion.github.io/publications_and_presentations/irion_dissertation.pdf), Ph.D. dissertation, University of California, Davis, Dec. 2015.

5. J. Irion and N. Saito, [Learning sparsity and structure of matrices with multiscale graph basis dictionaries](https://www.math.ucdavis.edu/~saito/publications/matanal.html), *Proc. 2016 IEEE 26th International Workshop on Machine Learning for Signal Processing (MLSP)*, (A. Uncini, K. Diamantaras, F. A. N. Palmieri, and J. Larsen, eds.), 2016.

6. J. Irion and N. Saito, [Efficient approximation and denoising of graph signals using the multiscale basis dictionaries](https://www.math.ucdavis.edu/~saito/publications/eadgsumbd.html), *IEEE Transactions on Signal and Information Processing over Networks*, Vol. 3, no. 3, pp. 607-616, 2017.

7. N. Saito, [How can we naturally order and organize graph Laplacian eigenvectors?](https://www.math.ucdavis.edu/~saito/publications/lapeigport.html) *Proc. 2018 IEEE Workshop on Statistical Signal Processing*, pp. 483-487, 2018.

8. Y. Shao and N. Saito, [The extended Generalized Haar-Walsh Transform and applications](https://www.math.ucdavis.edu/~saito/publications/eghwt.html), *Wavelets and Sparsity XVIII*, (D. Van De Ville, M. Papadakis, and Y. M. Lu, eds.), *Proc. SPIE 11138*, Paper #111380C, 2019.

9. H. Li and N. Saito, [Metrics of graph Laplacian eigenvectors](https://www.math.ucdavis.edu/~saito/publications/metgraphlap.html), *Wavelets and Sparsity XVIII*, (D. Van De Ville, M. Papadakis, and Y. M. Lu, eds.), *Proc. SPIE 11138*, Paper #111381K, 2019.

10. Y. Shao, [The Extended Generalized Haar-Walsh Transform and Applications](https://www.math.ucdavis.edu/~tdenena/dissertations/202008_Shao_Yiqun_dissertation.pdf), Ph.D. dissertation, University of California, Davis, Sep. 2020.

11. A. Cloninger, H. Li and N. Saito, [Natural graph wavelet packet dictionaries](https://www.math.ucdavis.edu/~saito/publications/ngwp.html), *J. Fourier Anal. Appl.*, vol. 27, Article \#41, 2021.

12. H. Li, Natural Graph Wavelet Dictionaries: Methods and Applications, Ph.D. dissertation, University of California, Davis, Jun. 2021.

13. N. Saito and Y. Shao, [eGHWT: The extended Generalized Haar-Walsh Transform](https://www.math.ucdavis.edu/~saito/publications/eghwt21.html), *J. Math. Imaging Vis.*, vol. 64, no. 3, pp. 261-283, 2022.