astro-informatics / s2wav

Differentiable and accelerated wavelet transform on the sphere with JAX

Differentiable and accelerated wavelet transform on the sphere

S2WAV is a JAX package for computing wavelet transforms on the sphere and rotation group. It leverages autodiff to provide differentiable transforms, which are also deployable on modern hardware accelerators (e.g. GPUs and TPUs), and can be mapped across multiple accelerators.

More specifically, S2WAV provides support for scale-discretised wavelet transforms on the sphere and rotation group (for both real and complex signals), with support for adjoints where needed, and comes with a variety of different optimisations (e.g. precompute or not, multi-resolution algorithms) that one may select depending on available resources and desired angular resolution $L$. S2WAV is a sister package of S2FFT, both of which are part of the SAX project, which aims to provide comprehensive support for differentiable transforms on the sphere and rotation group.

Wavelet Transform ⚡

S2WAV is an updated implementation of the scale-discretised wavelet transform on the sphere, which builds upon the papers of Leistedt et al 2013 and McEwen et al 2017. This wavelet transform is designed to have excellent localisation and uncorrelation properties, and has been successfully adopted for various applications e.g. scattering transforms on the sphere McEwen et al 2022. The wavelet dictionary is constructed by tiling the harmonic line with infinitely differentiable Cauchy-Schwartz functions, which can straightforwardly be performed in an efficient multiresolution manner, as in the Euclidean case. This is what the directional wavelet filters look like in pixel space.

Installation 💻

The Python dependencies for the S2WAV package are listed in the file requirements/requirements-core.txt and will be automatically installed into the active python environment by pip when running

pip install .        

from the root directory of the repository. Unit tests can then be executed to ensure the installation was successful by running

pytest tests/

In the near future one will be able to install S2WAV directly from PyPi by pip install s2wav but this is not yet supported. Note that to run JAX on NVIDIA GPUs you will need to follow the guide outlined by Google.

Usage 🚀

To import and use S2WAV is as simple follows:

import s2wav 

# Compute wavelet coefficients
f_wav, f_scal = s2wav.analysis(f, L, N)

# Map back to signal on the sphere 
f = s2wav.synthesis(f_wav, f_scal, L, N)

however we strongly recommend that the multiresolution argument is set to true, as this will accelerate the transform by a factor of the total number of wavelet scales, which can be around an order of magnitude.

Contributors ✨

We strongly encourage contributions from any interested developers; a simple example would be adding support for new wavelet filters e.g. spherical needlets Chan et al 2016 or spherical ridgelets McEwen & Price 2020! Thanks goes to these wonderful people (emoji key):

Matt Price 💻 👀 📖 🎨

Jason McEwen 👀 🎨

Alicja Polanska 💻 👀

Jessica Whitney 💻 👀

Attribution

A BibTeX entry for S2WAV is:

@article{price:s2wav, 
   author = {Matthew A. Price and Alicja Polanska and Jessica Whitney and Jason D. McEwen},
    title = {"Differentiable and accelerated directional wavelet transform on the sphere and ball"},
   eprint = {arXiv:2402.01282},
     year = {2024}
}

License 📝

Copyright 2024 Matthew Price, Jessica Whtiney, Alicja Polanska, Jason McEwen and contributors.

S2WAV is free software made available under the MIT License. For details see the LICENSE file.