Fast spin ±2 spherical harmonics transforms and application in cosmology

✍ Scribed by Y. Wiaux; L. Jacques; P. Vandergheynst

• Book ID: 104021680
• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 474 KB
• Volume: 226
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2007.07.005

✦ Synopsis

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 OðL 2 log 2 2 LÞ, 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 OðL 3 Þ 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.