What are scattering transforms?¶
The scattering transform is a wavelet-based representation that captures non-Gaussian statistical properties of a signal across multiple scales. Unlike the power spectrum, which only encodes second-order (Gaussian) information, scattering coefficients preserve higher-order correlations -- making them ideal for characterising complex, non-Gaussian fields such as those found in astrophysics and geoscience.
The method was introduced by Mallat (2012) and adapted to spherical astrophysical data by Delouis et al. 2022, who applied it to CMB component separation using the FOSCAT library.
Why this matters for astrophysics¶
Large Scale Structure (LSS) maps encode the distribution of matter in the Universe. Standard two-point statistics (power spectra) lose information about the non-Gaussian features imprinted by gravitational collapse. By matching scattering coefficients rather than power spectra alone, we can synthesise realisations that faithfully reproduce the full statistical complexity of the observed field.
The FIESTA cross-domain story¶
This repository is one half of a cross-domain demonstration within the FIESTA-OSCARS project. We show that the same scattering transform methodology transfers between:
Astrophysics (this repo) -- synthesis of an LSS cosmological map
Earth observation (fiesta
-scattering -sst) -- synthesis of a Sea Surface Temperature field
The mathematical framework is identical; only the input data and physical interpretation change. This transferability is a concrete example of how FAIR, reproducible research workflows can bridge scientific disciplines.
Results summary¶
| Metric | Value |
|---|---|
| Power spectrum ratio (synthesised / input) | 0.987 |
| Scattering coefficient match | 99.6 % |
The synthesised map reproduces both the power spectrum and the higher-order scattering statistics of the original LSS field to high fidelity.
FORRT nanopublication chain¶
The full provenance of this replication is recorded as a six-step FORRT nanopublication chain on the Science Live platform — paper → quote → atomic claim → FORRT claim → study → outcome → CiTO citation back to the paper. Each step is independently citable and machine-readable.
Headline assertion — machine-readable: This replication
cito:confirmsandcito:usesMethodInDelouis et al. 2022Two relationships in one citation nanopublication: we substantiate the paper’s generalisation claim (
cito:confirms) by replicating the framework on a different astrophysical map, and our work uses the scattering-transform method developed in that paper (cito:usesMethodIn). Discovery tools (Scholia, Wikidata pipelines, SPARQL endpoints) can follow this single citation to find both relationships.
The five preceding nanopubs build the provenance ladder up to that citation:
| Step | Type | Nanopub URI |
|---|---|---|
| 1 | Quote-with-comment | https:// |
| 2 | AIDA sentence | https:// |
| 3 | FORRT Claim (model performance) | https:// |
| 4 | FORRT Replication Study | https:// |
| 5 | FORRT Replication Outcome (Validated, High) | https:// |
| 6 | CiTO confirms + usesMethodIn Delouis 2022 | https:// |
Companion repositories¶
fiesta
-scattering -sst -- Sea Surface Temperature synthesis (Earth observation counterpart) FOSCAT -- the scattering transform library by Jean-Marc Delouis
- Delouis, J.-M., Allys, E., Gauvrit, E., & Boulanger, F. (2022). Non-Gaussian modelling and statistical denoising of Planck dust polarisation full-sky maps using scattering transforms. Astronomy & Astrophysics, 668, A122. 10.1051/0004-6361/202244566