The Blind Deconvolution of Linearly Blurred Images using non-Parametric Stabilizing Functions

Abstract

An iterative solution to the problem of blind image deconvolution is presented whereby a previous image estimate is explicitly used in the new image estimation process. The previous image is pre-filtered using an adaptive, non-parametric stabilizing function that is updated based on a current error estimate. This function is experimentally shown to dramatically benefit the convergence rate for the a priori restoration case. Noise propagation from one iteration to the next is reduced by the use of a second, regularizing operator, resulting in a hybrid iteration technique. Further, error terms are developed that shed new light on the error propagation properties of this method and others by quantifying the extent of noise and regularization error propagation. Optimal non-parametric, frequency adaptive stabilizing and regularization functions are then derived based on this error analysis.