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Fast spin +-2 spherical harmonics transforms and application in cosmology

Y. Wiaux·L. Jacques·P. Vandergheynst
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Abstract

A fast and exact algorithm is developed for the spin +-2 spherical harmonics transforms on equi-angular pixelizations on the sphere. It is based on the Driscoll and Healy fast scalar spherical harmonics transform. The theoretical exactness of the transform relies on a sampling theorem. The associated asymptotic complexity is of order O(L^2 log^2_2(L)), where 2L stands for the square-root of the number of sampling points on the sphere, also setting a band limit L for the spin +-2 functions considered. The algorithm is presented as an alternative to existing fast algorithms with an asymptotic complexity of order O(L^3) on other pixelizations. We also illustrate these generic developments through their application in cosmology, for the analysis of the cosmic microwave background (CMB) polarization data.

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Y. Wiaux, L. Jacques, P. Vandergheynst. 2007-08-14. Fast spin +-2 spherical harmonics transforms and application in cosmology. https://doi.org/10.1016/j.jcp.2007.07.005

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