FOSCAT

FOSCAT is a Python package for wavelet/scattering-based analysis and synthesis of data on regular 2D grids and on the sphere with HEALPix pixelization.

This README replaces the former dependency on FOSCAT_DEMO. The recommended examples are now the notebooks from demo-foscat-pangeo-eosc, especially:

• Demo_Synthesis.ipynb - global HEALPix synthesis from scattering-covariance statistics.
• Synthesis2D.ipynb - 2D image/field synthesis.
• Denoising-2D.ipynb - denoising by statistical constraints.
• Remove_CMB.ipynb - component separation / CMB-like background removal.
• local_foscat.ipynb and CNN_local.ipynb - local HEALPix domains and local spherical convolutions.

Install

pip install foscat

For the examples, a fuller environment is usually useful:

micromamba create -n foscat python=3.10
micromamba activate foscat
pip install foscat
pip install tensorflow torch healpy xarray gcsfs zarr jupyterlab

Minimal HEALPix synthesis sketch

import numpy as np
import foscat.scat_cov as sc
from foscat.Synthesis import Synthesis

nside = 64
target_map = np.random.randn(12 * nside**2)

scat_op = sc.funct(KERNELSZ=5, NORIENT=4, OSTEP=1, all_type='float64')
target_stat = scat_op.eval(target_map)

class MyLoss:
    def __init__(self, scat_op, target_stat):
        self.scat_op = scat_op
        self.target_stat = target_stat

    def eval(self, x, batch, return_all=False):
        stat = self.scat_op.eval(x)
        loss = stat.reduce_mean_batch((stat - self.target_stat) ** 2)
        return loss

x0 = np.random.randn(target_map.size)
solver = Synthesis(MyLoss(scat_op, target_stat))
result = solver.run(x0, EVAL_FREQUENCY=10, NUM_EPOCHS=50)

Documentation

This repository contains a MkDocs documentation skeleton:

pip install mkdocs mkdocs-material
mkdocs serve

A minimal Sphinx bridge is also provided in docs_sphinx/ for teams preferring Sphinx.

Main sections

• Getting started: installation and concepts.
• User guide: scattering covariance, HEALPix synthesis, 2D synthesis, component separation, and local wavelet convolutions.
• Examples: mapping from maintained notebooks to documentation pages.
• Reference: practical API entry points and best practices.