## A fast algorithm for filtering and wavelet decomposition on the sphere

Martin Böhme and Daniel Potts

### Abstract

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 Transforms, 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 ${\cal O}(N^2\log N)$ operations for ${\cal O}(N^2)$ 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.

Full Text (PDF) [540 KB]

### Key words

spherical filter, spherical Fourier transform, spherical harmonics, associated Legendre functions, fast discrete transforms, fast Fourier transform at nonequispaced knots, wavelets, fast discrete summation.

### AMS subject classifications

65Txx, 33C55, 42C10.

< Back