HierArchical Wavelet Coefficients on the Sphere (HAWCS): the Scattering Transform on Spherical Maps
Abstract
Extracting Gaussian information from data is well understood, but characterizing non-Gaussianity is challenging. We introduce HAWCS, a healpy-based Python package for efficiently computing wavelet scattering transform coefficients from full-sky maps. These coefficients provide compact summary statistics that are sensitive to higher-order structure and interactions across angular scales. We test the implementation on controlled Gaussian and non-Gaussian fields and demonstrate its computational efficiency. We then apply HAWCS to thermal Sunyaev-Zeldovich maps derived from Planck observations and four simulations, quantifying and comparing their higher-order statistical properties. We also use the method to expose the signatures of gravitational lensing in cosmic microwave background (CMB) temperature maps. These results demonstrate that HAWCS is a practical tool for validating component-separation pipelines and cosmological simulations, and a promising summary statistic for characterizing non-Gaussian structures beyond the power spectrum. These coefficients could also be used to constrain or generate simulated maps that reproduce the same statistical features of real data.
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BibTeX
@misc{abghari2026hierarchical,
title = {{HierArchical Wavelet Coefficients on the Sphere (HAWCS): the Scattering Transform on Spherical Maps}},
author = {Arefe Abghari and Lukas T Hergt and Douglas Scott and Raelyn M Sullivan},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25548},
eprint = {2609.25548},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05781263v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - HierArchical Wavelet Coefficients on the Sphere (HAWCS): the Scattering Transform on Spherical Maps
AU - Arefe Abghari
AU - Lukas T Hergt
AU - Douglas Scott
AU - Raelyn M Sullivan
PY - 2026
DA - 2026/09/22
PB - HAL
DO - 10.48550/arxiv.2609.25548
UR - https://hal.science/hal-05781263v1
AB - Extracting Gaussian information from data is well understood, but characterizing non-Gaussianity is challenging. We introduce HAWCS, a healpy-based Python package for efficiently computing wavelet scattering transform coefficients from full-sky maps. These coefficients provide compact summary statistics that are sensitive to higher-order structure and interactions across angular scales. We test the implementation on controlled Gaussian and non-Gaussian fields and demonstrate its computational efficiency. We then apply HAWCS to thermal Sunyaev-Zeldovich maps derived from Planck observations and four simulations, quantifying and comparing their higher-order statistical properties. We also use the method to expose the signatures of gravitational lensing in cosmic microwave background (CMB) temperature maps. These results demonstrate that HAWCS is a practical tool for validating component-separation pipelines and cosmological simulations, and a promising summary statistic for characterizing non-Gaussian structures beyond the power spectrum. These coefficients could also be used to constrain or generate simulated maps that reproduce the same statistical features of real data.
ER -