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Combined model-based and data-driven approaches for inverse problems in imaging


   Department of Mathematical Sciences

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  Dr Tatiana Bubba  No more applications being accepted  Competition Funded PhD Project (UK Students Only)

About the Project

The University of Bath is inviting applications for the following PhD project commencing in October 2023.

Overview of the Research:

Inverse problems are ubiquitous in science and engineering, appearing whenever a physical quantity has to be reconstructed from indirect measurements. They are especially known for medical imaging (computed tomography, magnetic resonance imaging, etc.) but also in many other areas, including non-destructive material testing and computer vision.

In many problems, measurements are scarce and noisy, yielding an unstable reconstruction and the need to complement the insufficient data with some prior information which may be available on the solution. Traditionally this has been achieved with (model-based) regularisation, with sparsity promoting regularisation becoming dominant in the last decades. More recent studies have demonstrated that data-driven approaches (such as deep learning) can exhibit superior performance for incorporating prior information in the solution of inverse problems, despite their lack of provable theoretical guarantees.

The goal of this applied research project is to develop neural network architectures, together with their implementation, that combine the best of both worlds exploring the interplay between traditional model-based regularisation approaches and data-driven methods applied to notable inverse problems, such as computed tomography [1,2].

The successful candidate will be part of the Numerical Analysis and Data Science group at the University of Bath, which offers a lively international and interdisciplinary environment (see https://bath-numerical-analysis.github.io).

This is an exceptional opportunity to conduct ambitious research and to collaborate with an international team at the forefront of the interface between mathematics, computational imaging and machine learning. Researchers trained in this interface are in high demand both in academia and industry.

Project keywords: inverse problems, machine learning, deep learning, imaging, optimisation, regularisation. 

Candidate Requirements:

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

The ideal candidate will have experience in one or more of the following areas: inverse problems, machine learning, mathematical imaging, variational methods and/or optimisation. Experience in programming is highly desirable (e.g. MATLAB / Python, Tensorflow / PyTorch). The ideal candidate should also have strong communication and organisation skills and be a team player.

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

Enquiries and Applications:

Informal enquiries are welcomed and should be directed to Dr Tatiana Bubba 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 prior to the application deadline of Sunday 22 January 2023.

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

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.

Exceptional Overseas students (e.g. with a UK Master’s Distinction or international equivalent and relevant research experience), who are interested in this project, should contact the lead supervisor in the first instance to discuss the possibility of applying for supplementary funding.

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.


Funding Notes

A studentship includes Home tuition fees, a stipend (£17,668 per annum, 2022/23 rate) and research/training expenses (£1,000 per annum) for up to 3.5 years. Eligibility criteria apply – see Funding Eligibility section above.

References

[1] Bubba T.A., Kutyniok G., Lassas M., März M., Samek W., Siltanen S. and Srinivasan V., Learning the invisible: a hybrid deep learning-shearlet-based framework for limited angle tomography, Inverse Problems 35, 064002
[2] Bubba T.A., Galinier M., Lassas M., Prato M., Ratti L. and Siltanen S., Deep neural networks for inverse problems with pseudodifferential operators: an application to limited-angle tomography, SIAM Journal on Imaging Sciences 14(2), 470-505.

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