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Fast wavelet transform on the ball

Project description


The FLAGLET code provides functionality to perform fast and exact wavelet transform on the ball. More details may be found in the extensive documentation.


First install FLAGLET for python by running

pip install pyflaglet

Then you can call it from any python script to perform forward and inverse flaglet transforms and their adjoints by

import pyflaglet as flaglet
import numpy as np

parameters = flaglet.flaglet_parameters(specify_parameters)

# Create a random complex signal (c indexing)
f_size = flaglet.flaglet_f_dim(parameters)
rng = np.random.default_rng()
f = rng.normal(size=(f_size)) + 1j*rng.normal(size=(f_size))

# Compute e.g. the Forward transform
f_wav, f_scal = flaglet.flaglet_forward(f, parameters)


B. Leistedt, J. D. McEwen, and M. A. Price


    author  = {Matthew~A.~Price and Jason~D.~McEwen},
    title   = {Bayesian variational regularization on the ball},
    journal = {ArXiv},
    eprint  = {arXiv:2105.05518},
    year    = 2021
    author  = {Boris~Leistedt and Jason~D.~McEwen},
    title   = {Exact Wavelets on the Ball},
    journal = {IEEE Trans. Sig. Proc.},
    year    = 2012,
    volume  = {60},
    number  = {12},
    pages   = {6257-6269},
    doi     = {10.1109/TSP.2012.2215030},
    author  = {Jason~D.~McEwen and Yves~Wiaux},
    title   = {A novel sampling theorem on the sphere},
    journal = {IEEE Trans. Sig. Proc.},
    year    = 2011,
    volume  = {59},
    number  = {12},
    pages   = {5876-5887},
    doi     = {10.1109/TSP.2011.2166394},
    author  = {Boris~Leistedt and Jason~D.~McEwen and Thomas~D.~Kitching and Hiranya~V.Peiris},
    title   = {3D weak lensing with spin wavelets on the ball},
    journal = {Physical Review D.},
    year    = 2015,
    volume  = {92},
    number  = {12},
    pages   = {123010},
    doi     = {10.1103/PhysRevD.92.123010},
    author  = {Jason~D.~McEwen and Martin~Büttner and Boris~Leistedt and Hiranya~V.Peiris and Yves~Wiaux},
    title   = {A Novel Sampling Theorem on the Rotation Group},
    journal = {IEEE Sig. Proc. Letters},
    year    = 2015,
    volume  = {22},
    number  = {12},
    pages   = {2425-2429},
    doi     = {10.1109/LSP.2015.2490676},
    author  = {Jason~D.~McEwen and Boris~Leistedt and Martin~Büttner and Hiranya~V.Peiris and Yves~Wiaux },
    title   = {Directional spin wavelets on the sphere},
    journal = {arXiv e-prints},
    eprint  = {1509.06749},
    year    = 2015,
    title   = {S2LET: A code to perform fast wavelet analysis on the sphere},
    author  = {Boris~Leistedt and Jason~D.~McEwen and Pierre~Vandergheynst and Yves~Wiaux},
    journal = {Astronomy & Astrophysics},
    volume  = {558},
    pages   = {A128},
    year    = 2013,


FLAGLET is released under the GPL-3 license (see LICENSE.txt).

FLAGLET package to perform fast wavelet transform on the sphere<br>
Copyright (C) 2021 Boris Leistedt & Jason McEwen & Matthew Price

This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
GNU General Public License for more details (LICENSE.txt).

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
MA  02110-1301, USA.

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