S2DW

"The S2DW code provides functionality to perform the scale discretised wavelet transform on the sphere developed in our paper: Exact reconstruction with directional wavelets on the sphere (ArXiv|DOI). Routines are provided to compute wavelet and scaling coefficients from the spherical harmonic coefficients of a signal on the sphere and to synthesise the spherical harmonic coefficients of the original signal from its wavelet and scaling coefficients. The reconstruction of the spherical harmonic coefficients of the original signal is exact to numerical precision. Typically, maximum reconstruction errors are of the order 10^(-12) or smaller. Please see our paper for further details of the wavelet transform and a discussion of typical reconstruction errors and execution times of this implementation.
It is considerably more accurate and efficient to perform our wavelet transform on the sphere in harmonic space, hence this is the approach adopted in the S2DW code. The S2DW library itself considers only the spherical harmonic representation of data defined on the sphere and not real space representations. Many different pixelisations schemes for the sphere exist, with corresponding algorithms to perform forward and inverse spherical harmonic transforms. These algorithms are not always exact, hence the core functionality of the S2DW code operates on the spherical harmonic coefficients of signals only. Users are then free to use any pixelisation of the sphere and the computation of spherical harmonic coefficients is the users' concern.

A number of optional utility programs are also provided in the S2DW code. These enable users to perform the scale discretised wavelet transform on data defined on the sphere in real space. The HEALPix pixelisation of the sphere is adopted for this purpose. The spherical harmonic transform on a HEALPix pixelisation is not exact, hence the reconstruction accuracy of our S2DW code for real space data is limited by the accuracy of the forward and inverse spherical harmonic transforms provided by HEALPix."

http://astro-informatics.github.io/s2dw/

https://arxiv.org/abs/1308.5706