  A new construction of a directional continuous wavelet analysis on the sphere
is derived herein. We adopt the harmonic scaling idea for the spherical
dilation operator recently proposed by Sanz et al. but extend the analysis to a
more general directional framework. Directional wavelets are a powerful
extension that allow one to also probe oriented structure in the analysed
function. Our spherical wavelet methodology has the advantage that all
functions and operators are defined directly on the sphere. The construction of
wavelets in our framework is demonstrated with an example.
