Extensions

Pycsou’s core functionalities can be extended via the following specialised extension modules.

Pycsou-sphere

Pycsou-sphere is an extension module for solving linear inverse problems on the sphere. The extension offers implementations of spherical zonal convolution operators as well as the spherical harmonic and Fourier-Legendre transforms (all compatible with Pycsou’s interface for linear operators). It also provides numerical routines for computing the Green kernels of common spherical pseudo-differential operators and generating spherical meshes/point sets.

This module heavily relies and follows similar conventions as the healpy package for spherical signal processing with Python.

The package (available on PyPI under the name pycsphere) is organised as follows:

  1. The subpackage pycsphere.linop implements the following common spherical linear operators:

    • Convolution/pooling operators,

    • Spherical transforms and their inverses,

    • Finite-difference spherical differential operators.

  2. The subpackage pycsphere.mesh provides routines for generating spherical meshes.

  3. The subpackage pycsphere.green provides numerical routines for computing the Green kernels of common spherical pseudo-differential operators.

The package’s documentation is available at this link.

Pycsou-gsp

Pycsou-gsp is the graph signal processing extension of Pycsou. The extension offers implementations of graph convolution and differential operators, compatible with Pycsou’s interface for linear operators. Such tools can be useful when solving linear inverse problems involving signals defined on non Euclidean discrete manifolds.

Graphs in Pycsou-gsp are instances from the class pygsp.graphs.Graph from the pygsp library for graph signal processing with Python.

The package (available on PyPI under the name pycgsp) is organised as follows:

  1. The subpackage pycgsp.linop implements the following common graph linear operators:

    • Graph convolution operators: GraphConvolution

    • Graph differential operators: GraphLaplacian, GraphGradient, GeneralisedGraphLaplacian.

  2. The subpackage pycgsp.graph provides routines for generating graphs from discrete tessellations of continuous manifolds such as the sphere.

The package’s documentation is available at this link.