Inverse Problems in Multi-Modality Imaging

   Department of Mathematical Sciences

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  Dr Matthias Ehrhardt  No more applications being accepted  Funded PhD Project (UK Students Only)

About the Project

The University of Bath is inviting applications for the following funded PhD project to commence as soon as possible and by September 2024 at the latest.

Overview of the Research:

In modern imaging applications, we often collect a range of measurements corresponding to different physical properties of the same object. These measurements may have different resolutions, different signal to noise levels and probe different material properties such as its elemental composition or overall density. While these are ultimately linked together as they probe the same sample, mathematically we currently treat them as different measurements and we don’t exploit at all the synergy between them. Specifically, this project focuses on mathematical models and algorithms to maximize the potential of multi-modality data. More generally, this project sits on the interface of inverse problems, optimization and machine learning. 

This is a collaborative project between the Department for Mathematical Sciences at the University of Bath and the Ada Lovelace Centre.

The studentship is part of the SAMBa Centre for Doctoral Training cohort. This is a four-year doctoral training programme that encompasses broad training and specialist research. Initially students will take courses across a spectrum of deterministic, probabilistic and statistical mathematical fields, receive training in machine learning, engage in student-led symposia, interdisciplinary research group projects, and participate in problem formulation workshops called ITTs (Integrative Think Tanks). The initial training will support development of the scope of the thesis. From 6-9 months, students will be primarily conducting thesis research, with continued engagement in SAMBa activities to develop leadership skills and research outlook.

The successful student will embed in a stimulating research environment in Bath, benefiting from the Centre for Mathematics and Algorithms for Data as well as the Bath Numerical Analysis and Data Science Group. Over the course of their PhD, the student will spend some time working at the Rutherford Appleton Laboratory (a short journey from Bath), collaborating with the scientists at the facility in progressing the research project.

Project keywords: imaging, inverse problems, multi-modality, X-rays, numerical analysis

Candidate Requirements:

Applicants should hold, or expect to receive, a First Class or good Upper Second Class UK Honours degree (or the equivalent) in mathematics or a closely related discipline. A master’s level qualification would also be advantageous.

The ideal candidate will have some experience in inverse problems or numerical methods but training can be provided for a suitably motivated candidate. Experience in programming is desirable (e.g., MATLAB/Python).

Non-UK applicants must meet our English language entry requirement.

Enquiries and Applications:

Informal enquiries are encouraged and should be directed to Dr Matthias Ehrhardt on email address [Email Address Removed].

Formal applications should be submitted via the University of Bath’s online application form for a PhD in Mathematics.

When completing the form, please ensure that you quote your preferred start date. Also, in the 'Funding your studies' section, please select 'CDT' from the first drop-down list, and 'Industry Sponsor' from the second drop-down list, and specify SAMBa and Ada Lovelace Centre in the text box. In the 'Your PhD project' section, please state the project title and supervisor's name in the appropriate boxes.

More information about applying for a PhD at Bath may be found on our website.

NOTE: Applications may close earlier than the advertised deadline if a suitable candidate is found; therefore, we recommend that you contact Dr Matthias Ehrhardt prior to applying and submit your formal application as early as possible.

Funding Eligibility:

To be eligible for funding, you must qualify as a Home student. The eligibility criteria for Home fee status are detailed and too complex to be summarised here in full; however, as a general guide, the following applicants will normally qualify subject to meeting residency requirements: UK and Irish nationals (living in the UK or EEA/Switzerland), those with Indefinite Leave to Remain and EU nationals with pre-settled or settled status in the UK under the EU Settlement Scheme. This is not intended to be an exhaustive list. Additional information may be found on our fee status guidance webpage, on the GOV.UK website and on the UKCISA website.

Equality, Diversity and Inclusion:

We value a diverse research environment and aim to be an inclusive university, where difference is celebrated and respected. We welcome and encourage applications from under-represented groups.

If you have circumstances that you feel we should be aware of that have affected your educational attainment, then please feel free to tell us about it in your application form. The best way to do this is a short paragraph at the end of your personal statement.

Mathematics (25)

Funding Notes

The successful student will receive a PhD studentship covering Home tuition fees and providing a doctoral stipend (at least £18,622 per annum) for 4 years. Eligibility criteria apply – see Funding Eligibility section above.


[1] Ehrhardt, M. J. (2021). Multi-modality Imaging with Structure-Promoting Regularizers. Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging
[2] Ehrhardt, M. J., Gallagher, F. A., McLean, M. A., & Schönlieb, C. B. (2022). Enhancing the spatial resolution of hyperpolarized carbon-13 MRI of human brain metabolism using structure guidance. Magnetic Resonance in Medicine, 87(3), 1301–1312.

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