Wiener Filter for Isotropic Signal Fields

The images of a three dimensional scene taken at varying depths are regarded as reference stochastic processes on the unit sphere to formulate the normal equations for estimating the image at any given depth. These comprise a set of coupled linear integral equations on the unit sphere for the filter bank. The coefficient functions of these equations are the scene correlations which are assumed to be known. By exploiting properties of the action of the rotation group on the unit sphere, this set of coupled integral equations is converted into a set of Wiener-Hopf convolutional integral equations on the rotation group. These are solved using the Peter-Weyl theory of the Fourier transform on the rotation group.