From global to regional analysis of the magnetic field on the sphere using wavelet frames

Wavelet analysis has proven to be a powerful tool for numerical studies and signal processing. The wavelets power lies in the fact that in general they only require a small number of coefficients to represent functions and large datasets accurately up to a given precision. In this paper, we present a wavelet construction for scalar functions defined on the sphere. In particular, we show how spherical harmonics can be efficiently represented with spherical wavelets. The final goal of this approach is to model the magnetic field of the Earth simultaneously on global and regional scales.