Hyperparameter Selection for Bayesian Image Reconstruction by Mimicking Physical Crystallization

Although Bayesian theory has been successfully applied for count-limited medical image reconstruction in the past two decades, its wide applications in clinic has been hampered by its hyperparameter ${\beta}$ , which is traditionally determined by a trial-error style. To eliminate the cumbersome style, this work aims to present a selection method by mimicking the physical model of cooling down the temperature adaptively for an economic high-quality crystal. From the basic Bayes' law, the physical meaning of hyperparameter can be interpreted as the ratio of the data uncertainty (or variance ${\alpha}$ ) and the prior tolerance (or ${\sigma}$ ) by formulating the probability distribution functions (FDFs) of the data fidelity and prior expectation. Inspired by this idea, the prior tolerance ${\sigma}$ can be treated as the temperature of the texture patterns, and ${\beta}$ can be adjusted according to different texture pattern status by satisfying the condition of each PDF in the Bayes' Law during the iteration. In Simulated phantom study, realistic Poisson noise added to the pre-log transmission data model was used. Both phantom simulation and clinical patient data results show that the proposed method can provide comparable reconstructed image quality comparing to the conventional methods but with much less reconstruction time. It is observed that the parameter introduced to satisfy the prior's PDF is more sensitive to stop the iteration process.