On multiscale denoising of spherical functions: Basic theory and numerical aspects

The basic concepts of selective multiscale reconstruction of functions on the sphere from error affected data is outlined for scalar functions. The selective reconstruction mechanism is based on the premise that multiscale approximation can be well represented in terms of only a relatively small number of expansion coefficients at various resolution levels. A new proof, including non-bandlimited kernel functions, of the pyramid scheme is presented to efficiently remove the noise at different scales using a priori statistical information, i.e. knowledge of the covariance function.