Wavelets on the sphere: implementation and approximations
The authors continue the analysis of the continuous wavelet transform (CWT) on the 2-sphere, introduced by \textit{J.-P. Antoine} and \textit{P. Vandergheynst} [Appl. Comput. Harmon. Anal. 7, No. 3, 262-291 (1999; Zbl 0945.42023)]. First, they discuss directional spherical wavelets, i.e., spherical wavelets that are sensitive to directions. Using fast Fourier transforms, the authors compute spherical CWT for data given on a regular spherical grid. Numerical examples are presented. Finally, they establish conditions under which a reconstruction formula of the spherical CWT holds in strong \(L^p\) topology with \(1\leq p<\infty\).
scientific article; zbMATH DE number 1891400