Here is an new version of the paper featuring a fast wavelet on the sphere (and expecting a sparse decomposition on the sphere). : S2LET: A code to perform fast wavelet analysis on the sphere by B. Leistedt, J. D. McEwen, P. Vandergheynst, Y. Wiaux. The abstract reads:
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-depended features of signals on the sphere. The scale-discretised wavelet transform was developed previously and reduces to the needlet transform in the axisymmetric case. 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.The S2Let package is at: http://www.s2let.org/
From the introduction:
The S2LET code (ArXiv paper) provides high performance routines for fast wavelet analysis of signals on the sphere. It uses the SSHT code built on the MW sampling theorem (ArXiv | DOI) to perform exact spherical harmonic transforms on the sphere. The resulting wavelet transform implemented in S2LET is theoretically exact, i.e. a band-limited signal can be recovered from its wavelet coefficients exactly and the wavelet coefficients capture all the information. S2LET also supports the HEALPix sampling scheme, in which case the transforms are not theoretically exact but achieve good numerical accuracy.
This page outlines the main features of S2LET, installation details as well as the core functionalties and interfaces. References, version, and license information then follows. The S2LET code requires the SSHT and FFTW libraries. The IO FITS features require CFITSIO. To support HEALPix, a valid installation of its Fortran implementation must be provided.
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