  We present a framework for the optimal filtering of spherical signals
contaminated by realizations of an additive, zero-mean, uncorrelated and
anisotropic noise process on the sphere. Filtering is performed in the wavelet
domain given by the scale-discretized wavelet transform on the sphere. The
proposed filter is optimal in the sense that it minimizes the mean square error
between the filtered wavelet representation and wavelet representation of the
noise-free signal. We also present a simplified formulation of the filter for
the case when azimuthally symmetric wavelet functions are used. We demonstrate
the use of the proposed optimal filter for denoising of an Earth topography map
in the presence of additive, zero-mean, uncorrelated and white Gaussian noise,
and show that the proposed filter performs better than the hard thresholding
method and weighted spherical harmonic~(weighted-SPHARM) signal estimation
framework.
