zbMATH — the first resource for mathematics

A fast algorithm for filtering and wavelet decomposition on the sphere. (English) Zbl 1030.65148
Summary: This paper introduces a new fast algorithm for uniform-resolution filtering of functions defined on the sphere. We use a fast summation algorithm based on nonequispaced fast Fourier tansforms, building on previous work that used fast multipole methods. The resulting algorithm performs a triangular truncation of the spectral coefficients while avoiding the need for fast spherical Fourier transforms. The method requires \(O(N^2\log N)\) operations for \(O(N^2)\) grid points.
Furthermore, we apply these techniques to obtain a fast wavelet decomposition algorithm on the sphere. We present the results of numerical experiments to illustrate the performance of the algorithms.

65T60 Numerical methods for wavelets
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65T50 Numerical methods for discrete and fast Fourier transforms
Full Text: Link EuDML