Hyperparameter Estimation for Emission Computed Tomography Data

Over the last years many statistical models have been proposed to restore tomographical images. However, their use in medical environment has been limited due to several factors. These factors include the need of greater computational time than deterministic methods and the selection of the hyperparameters of in a given image model. Consequently, deterministic methods, like filtered back-projection (FBP) and algebraic reconstruction, are commonly used. In this work, we propose a method to estimate, from observed image data, the scale hyperparameter σ in a Generalized Gaussian Markov Random Field (GGMRF). The parameter σ determines the overall smoothness of the restoration, so its estimation has enormous interest. We use the hierarchical Bayesian paradigm and evidence analysis to obtain the proposed iterative estimation method. The method is tested on synthetic images.