Bayesian methods for medical image estimation

医学成像技术的使用在许多严重疾病的早期诊断和治疗中至关重要。在过去的20-30年里，成像速度和分辨率沿着有了重大的进步，同时成本也有了同样显著的下降。虽然图像重建，一个逆问题，可以被描述为一个统计问题，很少有人提出的方法已经找到了他们的方式进入临床实践。例如，第一篇推荐贝叶斯方法的论文出现在30多年前，但临床上最广泛使用的方法是40多年前的。即使是目前正在开发的方法，由于实际缺陷，在学术实践之外也进展缓慢。在所有这些情况下，一个关键问题是如何以自动的方式平衡来自数据的信息与先验信息，这种方式对先验模型假设与现实之间的不匹配具有鲁棒性。该项目将考虑一系列贝叶斯建模情况，从SPECT和PET数据的简单马尔可夫随机场先验，到PET/MR或PET/CT数据组合的混合内核方法。自动估计未知的先验参数以及图像重建将使用分层贝叶斯建模方法进行研究。类似地，扩展到非齐次模型将允许局部自适应方法。最重要的阶段将是纳入先前规格与现实之间不匹配的模型。每一种情况都有可能产生具有实际重要性的方法，因此该项目可以产生重大影响。通过项目主管，学生将有机会获得幻影和真实的数据集，涵盖各种各样的医疗应用和数据收集技术，以及具有重要实践经验的合作者。

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.