S2LET: A code to perform fast wavelet analysis on the sphere

¹ Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
e-mail: boris.leistedt.11@ucl.ac.uk
² Mullard Space Science Laboratory (MSSL), University College London, Surrey RH5 6NT, UK
e-mail: jason.mcewen@ucl.ac.uk
³ Institute of Electrical Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
e-mail: pierre.vandergheynst@epfl.ch
⁴ Department of Radiology and Medical Informatics, University of Geneva (UniGE), 1211 Geneva, Switzerland
⁵ Department of Medical Radiology, Lausanne University Hospital (CHUV), 1011 Lausanne, Switzerland
e-mail: yves.wiaux@epfl.ch
⁶ Institute of Sensors, Signals & Systems, Heriot Watt University, Edinburgh EH14 4AS, UK

Received: 13 November 2012
Accepted: 27 August 2013

Abstract

We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-dependent features of signals on the sphere. The reconstruction of a signal from its wavelets coefficients is made exact here through the use of a sampling theorem on the sphere. Moreover, a multiresolution algorithm is presented to capture all information of each wavelet scale in the minimal number of samples on the sphere. In addition S2LET supports the HEALPix pixelisation scheme, in which case the transform is not exact but nevertheless achieves good numerical accuracy. The core routines of S2LET are written in C and have interfaces in Matlab, IDL and Java. Real signals can be written to and read from FITS files and plotted as Mollweide projections. The S2LET code is made publicly available, is extensively documented, and ships with several examples in the four languages supported. At present the code is restricted to axisymmetric wavelets but will be extended to directional, steerable wavelets in a future release.