Automatic hyperparameter estimation in probabilistic image restoration algorithm based on Gibbs microcanonical distribution

For an original image given as an 8-gray-level image, the framework for image restoration is composed of Bayes statistics for the a priori probability distribution based on the microcanonical distribution. In this process, the a priori probability distribution serving as the microcanonical distribution is formulated on the basis of the variables characterizing the spatial flatness and smoothness of the image in terms of the number of nearest pixel pairs with different gray levels and the number of nearest pixel pairs with gray levels differing by 1. In the present paper, we propose a new method of estimation, from a degraded image, of the number of nearest pixel pairs with different gray levels and the number of nearest pixel pairs with gray levels differing by 1 in the original image. Then, based on that formulation, an iterative computation algorithm for the restoration of a 256-gray-level image is presented from the viewpoint of statistical mechanics. Through some numerical experiments, we investigate how the proposed method can improve the quality of the restored image.