  We present a joint SO(3)-spectral domain filtering framework using
directional spatially localized spherical harmonic transform (DSLSHT), for the
estimation and enhancement of random anisotropic signals on the sphere
contaminated by random anisotropic noise. We design an optimal filter for
filtering the DSLSHT representation of the noise-contaminated signal in the
joint SO(3)-spectral domain. The filter is optimal in the sense that the
filtered representation in the joint domain is the minimum mean square error
estimate of the DSLSHT representation of the underlying (noise-free) source
signal. We also derive a least-square solution for the estimate of the source
signal from the filtered representation in the joint domain. We demonstrate the
capability of the proposed filtering framework using the Earth topography map
in the presence of anisotropic, zero-mean, uncorrelated Gaussian noise, and
compare its performance with the joint spatial-spectral domain filtering
framework.
