Bayesian joint mixture framework for the integration of anatomical information in functional image reconstruction

We present a Bayesian joint mixture framework for integrating anatomical image intensity and region segmentation information into emission tomographic reconstruction in medical imaging. The joint mixture framework is particularly well suited for this problem and allows us to integrate additional available information such as anatomical region segmentation information into the Bayesian model. Since this information is independently available as opposed to being estimated, it acts as a good constraint on the joint mixture model. After specifying the joint mixture model, we combine it with the standard emission tomographic likelihood. The Bayesian posterior is a combination of this likelihood and the joint mixture prior. Since well known EM algorithms separately exist for both the emission tomography (ET) likelihood and the joint mixture prior, we have designed a novel EM2 algorithm that comprises two EM algorithms - one for the likelihood and one for the prior. Despite being dove-tailed in this manner, the resulting EM2 algorithm is an alternating descent algorithm that is guaranteed to converge to a local minimum of the negative log Bayesian posterior. Results are shown on synthetic images with bias/variance plots used to gauge performance. The EM2 algorithm resulting from the joint mixture framework has the best bias/variance performance when compared with six other closely related algorithms that incorporate anatomical information to varying degrees.