Locally-adaptive Bayesian modelling for medical image reconstruction


Contact Dr Robert G Aykroyd or Dr Charalampos Tsoumpas to discuss this project further informally.

Project description

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. This means that every major hospital has access to highly sophisticated equipment. 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, motivated by machine learning, 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.

Although this project does not have dedicated funding, all successful applicants without funding will be considered for a fully-funded scholarship, in an open competition across the entire School of Maths. To be considered for this funding, it is recommended to apply no later than 31st March 2018 for funding to start in October 2018. However, earlier applications are welcome, and will be considered on an ongoing basis.

Entry requirements

Applications are invited from candidates with or expecting a minimum of a UK upper second class honours degree (2:1), and/ or a Master's degree in a relevant subject such as (but not limited to) mathematics or statistics.

How to apply

Formal applications for research degree study should be made online through the university's website. Please state clearly in the research information section that the PhD you wish to be considered for is 'Locally-adaptive Bayesian modelling for medical image reconstruction’ as well as Dr Robert G Aykroyd as your proposed supervisor.

If English is not your first language, you must provide evidence that you meet the University’s minimum English Language requirements.

If you require any further information please contact the Graduate School Office
 e: math.pgr.admissions@leeds.ac.uk.

We welcome scholarship applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit.