On the choice of window for spatial smoothing of spherical data

This paper investigates spectral filtering using isotropic spectral windows, which is a computationally efficient method of spatial smoothing on the sphere. We propose a Slepian eigenfunction window, which is obtained as a solution of the concentration problem on the sphere, as a good choice of the window function. We also unify a comprehensive set of quantitative tools, both spatial and spectral, to assess and compare the performance of different smoothing windows (i.e., smoothers). We analyze and compare the performance of the proposed window against the two best available candidates in the literature: von-Hann window and von Mises-Fisher distribution window. We establish that the latter window includes the popular Gauss window as a subcase. We show that the Slepian eigenfunction window has the smallest spatial variance (better spatial localization) and the smallest side-lobe level.