The Bussgang algorithm for multichannel blind image restoration

This work derives the multichannel Bussgang restoration algorithm for blind image restoration problems. In its basic outline, the derived Bussgang restoration algorithm is based on iteratively filtering the measurements by means of a bank of FIR filters, and updating the filter-bank on the base of a nonlinear estimate of the original image. The filters are updated by solving a linear system (multichannel normal equations) whose coefficients' matrices depend on the cross-correlations between the measurements and a nonlinear estimate of the original image, this latter obtained using a Bayesian criterion. Experimental results pertaining to restoration of motion blurred text images and out-of-focus star field images are reported.