87281 20190316233751.0 10.1086/507692 doi 9601 DAR 000242125700074 ISI ARTICLE Fast directional correlation on the sphere with steerable filters 2006 2006 Journal Articles A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order O(L^5), where 2L stands for the square-root of the number of sampling points on the sphere, also setting a band limit L for the signals and filters considered. The filter steerability allows to compute the directional correlation uniquely in terms of direct and inverse scalar spherical harmonics transforms, which drive the overall asymptotic complexity. The separation of variables technique for the scalar spherical harmonics transform produces an O(L^3) algorithm independently of the pixelization. On equi-angular pixelizations, a sampling theorem introduced by Driscoll and Healy implies the exactness of the algorithm. The equi-angular and HEALPix implementations are compared in terms of memory requirements, computation times, and numerical stability. The computation times for the scalar transform, and hence for the directional correlation, of maps of several megapixels on the sphere (L~10^3) are reduced from years to tens of seconds in both implementations on a single standard computer. These generic results for the scale-space signal processing on the sphere are specifically developed in the perspective of the wavelet analysis of the cosmic microwave background (CMB) temperature (T) and polarization (E and B) maps of the WMAP and Planck experiments. As an illustration, we consider the computation of the wavelet coefficients of a simulated temperature map of several megapixels with the second Gaussian derivative wavelet. computational methods sphere cosmology CMB LTS2 Wiaux, Y. 163268 240427 Jacques, L. 182131 243987 Vandergheynst, P. 120906 240428 820 Astrophys. J. 652 URL http://www.journals.uchicago.edu/ApJ/ 250892 n/a http://infoscience.epfl.ch/record/87281/files/fastcorr-arXiv-astro-ph-0508516v2.pdf LTS2 252392 U10380 oai:infoscience.tind.io:87281 article STI GLOBAL_SET EPFL-ARTICLE-87281 Wiaux2005_1327/LTS EPFL PUBLISHED REVIEWED ARTICLE