Angular multiselectivity with spherical wavelets

Abstract

We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of real images, ranging from highly directional to fully isotropic ones, was quite intensively studied for the case of signals over the Euclidean space. However, the present paper is the first attempt to deal with this task in the case of spherical signals. A multiselectivity scheme, similar to that proposed for $\mathbb R^2$-functions, is presented.