Supervisor: Dr Matthias Ehrhardt
Partners: Ada Lovelace Centre, in partnership with Rutherford Appleton Laboratories
Image reconstruction (or the solution to an inverse problem) is a fundamental task in any scientific imaging investigation such as X-ray and neutron computed tomography in material sciences or position emission tomography in medical imaging. Many state-of-the-art methods frame the image reconstruction tasks as the solution to an optimisation problem which in turn can be solved by iterative algorithms. While tremendous advancements have been made in the field of inverse problems and optimisation over the last half century, both the modelling and the optimisation require the selection of hyperparameters. Thus, applying such algorithms in a new application domain requires expert knowledge. In this project we want to approach this task via machine learning thereby making advanced image reconstruction algorithms much more widely available and easier to use.
Keywords: Imaging, inverse problems, X-ray tomography, machine learning, numerical analysis, image reconstruction
Candidate Requirements
In addition to the SAMBa entrance requirements, the ideal candidate will have experience in one or more of the following areas: inverse problems, machine learning, 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).
Enquiries and Applications
Informal enquiries are encouraged and should be directed to supervisor Dr. Matthias Ehrhardt me549@bath.ac.uk.
Applications are open for entry in September 2025. 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 or proposal and the name of the lead supervisor in the appropriate box.
"The students at SAMBa were engaging and motivated, above all interested in solving real world problems with their skills. As a result of SAMBa we have taken huge strides forward in a new technique in the assessment of arthritis related to psoriasis and the effect of treatment.
"For a small company like ours, this research is vital in delivering our vision to create digital technologies that change what’s possible for clinicians and patients."
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.
"The collaboration between SAMBa, UNAM and CIMAT has strengthened us in tools and techniques to visualize new perspectives of development and collaboration with a focus on generating value for other institutions."
"Working with SAMBa students to relay how our industry understands the daily challenges in aerospace design and manufacture and for them to translate them into statistical/mathematical models and methods was a refreshing and rewarding concept."
“Alongside the specific potential benefits to applied flood and coastal risk management, I have seen first-hand that the SAMBa CDT produces high calibre doctoral graduates with excellent skills in problem formulation and collaborative problem solving...”
"We are working with SAMBa to develop new tools for managing risk by combining deterministic and probabilistic methods."
"We found participating in the ITT to be an unique and engaging environment for exchanging ideas and it was also good fun. Above all it produced some truly innovative thinking."
“We have a great track record of successful collaboration with SAMBa, as we share a common aim – applying the latest thinking in mathematics and statistics to solve real-world problems."