  In this paper, we present an optimal filter for the enhancement or estimation
of signals on the 2-sphere corrupted by noise, when both the signal and noise
are realizations of anisotropic processes on the 2-sphere. The estimation of
such a signal in the spatial or spectral domain separately can be shown to be
inadequate. Therefore, we develop an optimal filter in the joint
spatio-spectral domain by using a framework recently presented in the
literature --- the spatially localized spherical harmonic transform ---
enabling such processing. Filtering of a signal in the spatio-spectral domain
facilitates taking into account anisotropic properties of both the signal and
noise processes. The proposed spatio-spectral filtering is optimal under the
mean-square error criterion. The capability of the proposed filtering framework
is demonstrated with by an example to estimate a signal corrupted by an
anisotropic noise process.
