Supervisor: Dr Matthias Ehrhardt
Partners: National Physical Laboratory
The medical imaging technique Positron Emission Tomography (PET) is an important cornerstone in modern medicine allowing non-invasive, sensitive, and specific detection of disease. For example, PET is routinely used in the diagnosis of various cancers. Small metastases at the edge of the PET resolution limit are difficult to be correctly diagnosed with the current technology, leaving clinicians in a very difficult situation.
In this PhD project, we are investigating Bayesian inference backed by sound mathematical and statistical theory to tackle this problem. In particular, we use approaches based on convex optimisation to make it computationally efficient and thus translatable to current clinical applications. The project is supported by a highly interdisciplinary team consisting of mathematicians (Bath, Heriot-Watt), engineers, physicists (National Physical Laboratory) and medical professionals.
Project keywords: Mathematics, inverse problems, uncertainty quantification, medical imaging, Positron Emission Tomography
Candidate Requirements
In addition to the SAMBa entrance requirements, the ideal candidate would have undergraduate experience in one or more of the following areas: inverse problems, mathematical imaging, optimisation, or numerical methods, but training can be provided for a suitably motivated candidate. Experience in programming is desirable (e.g., MATLAB / Python).
Contact the SAMBa team at samba@bath.ac.uk if you are unsure about your eligibility and would like to discuss your potential application.
Enquiries and Applications
Informal enquiries are encouraged and should be directed to supervisor Dr Matthias Ehrhardt m.ehrhardt@bath.ac.uk
Applications are open for entry in September 2026. Apply via the University of Bath’s online application form for an Integrated PhD in Statistical Applied Mathematics. Early applications are encouraged.
IMPORTANT:
When completing the application form:
1. In the Finance section, enter ‘SAMBa’ when asked to name the scholarship or PhD studentship you wish to be considered for.
2. In the Your research interests section, quote the project title of this project at the top of your statement and the name of the lead supervisor in the appropriate box.
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There were a couple of ongoing personal research collaborations with Novartis in the Department of Mathematical Sciences that were brought together to develop a set of challenges for Novartis’s participation in ITT12. These consisted of questions exploring modelling and data integration in pharmacokinetics models, and finding effective routes to drug development for liver disease.
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