Maximum Entropy and Bayesian Approach in Tomographic Image Reconstruction and Restoration

Abstract

In this paper we propose a Bayesian approach with Maximum Entropy (ME) priors to solve an integral equation which arises in various image restoration and reconstruction problems. Our contributions in this paper are the following: i) We discuss the a priori probability distributions which are deduced from different a priori constraints when the principle of ME is used. ii) When the a priori knowledge is only the noise covariance matrix and the image total intensity, and when the maximum a posteriori (MAP) is chosen as the decision rule to determine the values of image pixels, we show that the solution may be obtained by minimizing a criterion in which the structural entropy of the image is used as a particular choice of a regularization functional. The discussion is illustrated with some simulated results.