Two iterative image restoration algorithms with applications to nuclear medicine

Two methods for recovering an image that has been degraded while being processed are presented. 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 allows control of the degree of sharpness and smoothness of the restored image. The second algorithm with weight matrices included allows 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. The application of these algorithms to nuclear medicine images is presented.