Bayesian methods for medical image estimation

The use of medical imaging techniques are critical in the early diagnosis and treatment of many serious conditions. Over the past 20-30 years there have been major advances in imaging speed and resolution along with equally dramatic decreases in cost. Although image reconstruction, an inverse problem, can be described as a statistical question, very few proposed methods have found their way into clinical practice. For example, the first paper recommending a Bayesian approach appeared more than 30 years ago, but the most widely used methods in the clinic are from more than 40 years ago. Even methods currently being developed are slow to progress beyond academic exercises because of practical drawbacks. In all of these cases, a critical issue is how to balance information from data with prior information in an automatic way which is robust to mismatches between prior model assumptions and reality. This project will consider a range of Bayesian modelling situations from simple Markov random field priors for SPECT and PET data, to hybrid kernel methods of combined PET/MR or PET/CT data. The automatic estimation of unknown prior parameters alongside image reconstruction will be investigated using a hierarchical Bayesian modelling approach. Similarly, extension to non-homogeneous models will allow locally adaptive methods. The most important stage will be to incorporate models for mismatch between prior specification and reality. Each of these cases has the potential to produce methods of practical importance and hence the project can have a major impact. Through the project supervisors, the student will have access to phantom and real data set covering a wide variety of medical applications and data collection techniques, and also to collaborators with significant practical experience.