Regularization theory in image restoration-the stabilizing functional approach

Several aspects of the application of regularization theory in image restoration are presented. This is accomplished by extending the applicability of the stabilizing functional approach to 2-D ill-posed inverse problems. Inverse restoration is formulated as the constrained minimization of a stabilizing functional. The choice of a particular quadratic functional to be minimized is related to the a priori knowledge regarding the original object through a formulation of image restoration as a maximum a posteriori estimation problem. This formulation is based on image representation by certain stochastic partial differential equation image models. The analytical study and computational treatment of the resulting optimization problem are subsequently presented. As a result, a variety of regularizing filters and iterative regularizing algorithms are proposed. A relationship between the regularized solutions proposed and optimal Wiener estimation is identified. The filters and algorithms proposed are evaluated through several experimental results