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SLEPLET

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SLEPLET is a Python package for the construction of Slepian wavelets in the spherical and manifold (via meshes) settings. The API of SLEPLET has been designed in an object-orientated manner and is easily extendible. Upon installation, SLEPLET comes with two command line interfaces - sphere and mesh - which allows one to easily generate plots on the sphere and a set of meshes using plotly.

To read more about Slepian wavelets please see the following publications

Sifting Convolution on the Sphere Slepian Scale-Discretised Wavelets on the Sphere Slepian Scale-Discretised Wavelets on Manifolds Slepian Wavelets for the Analysis of Incomplete Data on Manifolds

Installation

The recommended way to install SLEPLET is via pip

pip install sleplet

To install the latest development version of SLEPLET clone this repository and run

pip install -e .

This will install two scripts sphere and mesh which can be used to generate the figures in the associated papers.

Supported Platforms

SLEPLET has been tested with Python. Windows is not currently supported as SLEPLET relies on pyssht and pys2let which do not work on Windows. These can hopefully be replaced with s2fft and s2wav in the future when they are available on PyPI.

Example Usage

SLEPLET may be interacted with via the API or the CLIs.

API Usage

The following demonstrates the first wavelet (ignoring the scaling function) of the South America region on the sphere.

import sleplet

B, J, J_MIN, L = 3, 0, 2, 128

region = sleplet.slepian.Region(mask_name="south_america")
f = sleplet.functions.SlepianWavelets(L, region=region, B=B, j_min=J_MIN, j=J)
f_sphere = sleplet.slepian_methods.slepian_inverse(f.coefficients, f.L, f.slepian)
sleplet.plotting.PlotSphere(
    f_sphere,
    f.L,
    f"slepian_wavelets_south_america_{B}B_{J_MIN}jmin_{J_MIN+J}j_L{L}",
    normalise=False,
    region=f.region,
).execute()

Slepian Wavelet j=2

CLI Usage

The demonstrates the first wavelet (ignoring the scaling function) of the head region of a Homer Simpson mesh for a per-vertex normals field.

mesh homer -e 3 2 0 -m slepian_wavelet_coefficients -u -z

Slepian Mesh Wavelet Coefficients j=2

Documentation

See here for the documentation. This includes demonstrations of the figures from the associated papers along with the API documentation. Further examples are included in the examples folder.

Community Guidelines

We'd love any contributions you may have, please see the contributing guidelines.

Citing

If you use SLEPLET in your research, please cite the paper.

@article{Roddy2023,
  title   = {{SLEPLET: Slepian Scale-Discretised Wavelets in Python}},
  author  = {Roddy, Patrick J.},
  year    = 2023,
  journal = {Journal of Open Source Software},
  volume  = 8,
  number  = 84,
  pages   = 5221,
  doi     = {10.21105/joss.05221},
}

Please also cite S2LET upon which SLEPLET is built, along with SSHT in the spherical setting or libigl in the mesh setting.