Bayesian Approach with Entropy Prior for Open Systems

Abstract

The Bayesian approach Maximum a Posteriori (MAP) is discussed in the context of solving the image reconstruction problem in nuclear medicine: positron emission tomography (PET) and single photon emission computer tomography (SPECT). Two standard probabilistic forms, Gibbs and entropy prior probabilities, are analyzed. It is shown that both the entropy-based and Gibbs priors in their standard formulations result in global regularization when a single parameter controls the solution. Global regularization leads to over-smoothed images and loss of fine structures. Over-smoothing is undesirable, especially in oncology in diagnosis of cancer lesions of small size and low activity. To overcome the over-smoothing problem and to improve resolution of images, the new approach based on local statistical regularization is developed.

Keywords

• image reconstruction problem
• bayesian maximum a posteriori approach
• entropy prior probability
• global regularization
• local statistical regularization
• open systems