2 ITERATIVE IMAGE-RESTORATION ALGORITHMS WITH APPLICATIONS TO NUCLEAR-MEDICINE

The purpose of this paper is to present two methods for the recovering of an image that has been degraded while being processed. The restoration problem is formulated as a constrained optimization problem in which a measure of smoothness based on the second derivatives of the restored image is maximized subject to the constraint that noise energy is equal to the energy in the difference between the distorted and blurred images. The approach is based on the Lagrange multiplier method. The first algorithm reduces the problem to the computation of few discrete Fourier transforms and has the ability to control the degree of sharpness and smoothness of the restored image where the input parameter can be interactively chosen by the observer. The second algorithm with weight matrices included enables the handling of edges and flat regions in the image in a pleasing manner for the human visual system. In this case the iterative conjugate gradient method is used in conjunction with the discrete Fourier transform to minimize the Lagrangian function. Furthermore the application of these algorithms to Nuclear Medicine images is presented.