Fast Directional Continuous Spherical Wavelet Transform Algorithms

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 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 Goacuterski, provides a savings of O(radicN
_pix
) over a direct quadrature implementation for N
_pix
pixels on the sphere, and allows one to perform a directional spherical wavelet analysis of a 10
⁶
pixel map on a personal computer