Fast directional continuous spherical wavelet transform algorithms

Abstract

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.

10 pages, 3 figures, replaced to match version accepted by IEEE Trans. Sig. Proc

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• Compressed sensing for wide-field radio interferometric imaging
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• Wavelet reconstruction of E and B modes for CMB polarisation and cosmic shear analyses
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