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We describe S2LET, a fast and robust implementation of the scale-discretisedwavelet transform on the sphere. Wavelets are constructed through a tiling ofthe harmonic line and can be used to probe spatially localised, scale-dependedfeatures of signals on the sphere. The scale-discretised wavelet transform wasdeveloped previously and reduces to the needlet transform in the axisymmetriccase. The reconstruction of a signal from its wavelets coefficients is madeexact here through the use of a sampling theorem on the sphere. Moreover, amultiresolution algorithm is presented to capture all information of eachwavelet scale in the minimal number of samples on the sphere. In addition S2LETsupports the HEALPix pixelisation scheme, in which case the transform is notexact but nevertheless achieves good numerical accuracy. The core routines ofS2LET are written in C and have interfaces in Matlab, IDL and Java. Realsignals can be written to and read from FITS files and plotted as Mollweideprojections. The S2LET code is made publicly available, is extensivelydocumented, and ships with several examples in the four languages supported. Atpresent the code is restricted to axisymmetric wavelets but will be extended todirectional, steerable wavelets in a future release.

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