PyWPH is a Python package for computing and handling Wavelet Phase Harmonic (WPH) statistics. These statistics can be derived from both real and complex-valued 2D data (e.g., images). Calculations are GPU-accelerated using PyTorch (torch>=1.9.0). Refer to the PyTorch installation guide for setting up PyTorch.

• GPU-accelerated computations with support for low-memory GPUs through efficient chunk-based processing.
• Support for real and complex-valued 2D data.
• Cross-WPH statistics for cross-statistical analysis.
• Ready-to-use examples for syntheses (including multi-channel synthese in external repository) and statistical denoising

Install PyWPH via PyPI:

pip install pywph

Alternatively, install form source:

git clone https://github.com/bregaldo/pywph.git
cd pywph
pip install .

To uninstall:

pip uninstall pywph

Explore the following resources to get started:

• 📖 Tutorial: A step-by-step introduction to PyWPH.
• 📂 Examples folder: Basic examples for computing WPH coefficients and advanced applications such as synthesis and statistical denoising.
• 🖼️ Multi-channel synthesis examples are available in this repository.

For a detailed presentation of the WPH statistics implemented in this package, refer to the paper: arXiv:2208.03538.

If you use PyWPH in your research, please cite the following paper:

• Regaldo-Saint Blancard, B., Allys, E., Boulanger, F., Levrier, F., & Jeffrey, N. "A new approach for the statistical denoising of Planck interstellar dust polarization data", Astronomy & Astrophysics 649, L18 (2021). ArXiv: 2102.03160

@article{regaldo2021,
       author = {{Regaldo-Saint Blancard}, Bruno and {Allys}, Erwan and {Boulanger}, Fran{\c{c}}ois and {Levrier}, Fran{\c{c}}ois and {Jeffrey}, Niall},
        title = "{A new approach for the statistical denoising of Planck interstellar dust polarization data}",
      journal = {Astronomy \& Astrophysics},
         year = 2021,
        month = may,
       volume = {649},
          eid = {L18},
        pages = {L18},
          doi = {10.1051/0004-6361/202140503},
archivePrefix = {arXiv},
       eprint = {2102.03160},
 primaryClass = {astro-ph.CO},
}

• Mallat, S., Zhang, S., & Rochette, G. "Phase harmonic correlations and convolutional neural networks", Information and Inference: A Journal of the IMA, 9(3), 721–747. (2020). ArXiv: 1810.12136.
• Allys, E., Marchand, T., Cardoso, J.-F., Villaescusa-Navarro, F., Ho, S., & Mallat, S. "New Interpretable Statistics for Large Scale Structure Analysis and Generation", Physical Review D, 102(10), 103506. (2020). ArXiv: 2006.06298.
• Zhang, S., & Mallat, S. "Maximum Entropy Models from Phase Harmonic Covariances", Applied and Computational Harmonic Analysis, 53, 199–230 (2021). ArXiv: 1911.10017.
• Régaldo-Saint Blancard, B., Allys, E., Auclair, C., Boulanger, F., Eickenberg, M., Levrier, F., Vacher, L. & Zhang, S. "Generative Models of Multi-channel Data from a Single Example - Application to Dust Emission", The Astrophysical Journal, 943, 9 (2023) ArXiv: 2208.03538. Code.

This package took inspiration from https://github.com/Ttantto/wph_quijote.

• New default discretization grid for the shift vector $\tau$.
• New set of scaling moments $L$ (which replaced the old ones).
• Version used in arXiv:2208.03538.

• Added cross-WPH statistics.
• Smarter way to evaluate moments at different $\tau$.
• Improved computation for non-periodic boundary conditions data.

• Initial release, corresponding to arXiv:2102.03160.