  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.
