  We describe the construction of a spherical wavelet analysis through the
inverse stereographic projection of the Euclidean planar wavelet framework,
introduced originally by Antoine and Vandergheynst and developed further by
Wiaux et al. Fast algorithms for performing the directional continuous wavelet
analysis on the unit sphere are presented. The fast directional algorithm,
based on the fast spherical convolution algorithm developed by Wandelt and
Gorski, provides a saving of O(sqrt(Npix)) over a direct quadrature
implementation for Npix pixels on the sphere, and allows one to perform a
directional spherical wavelet analysis of a 10^6 pixel map on a personal
computer.
