Student
Seb Scott

Seb graduated from the University of Bath in 2020 with an MMath , where he developed a keen interest in numerical analysis.

Seb graduated from the University of Bath in 2020 with an MMath , where he developed a keen interest in numerical analysis. His Master’s dissertation on “efficient prior conditioning for edge enhancement in imaging” involved the regularisation of discrete ill-posed linear inverse problems. He is looking forward to exploring the topics of both machine learning and data assimilation. Other than maths, Seb also enjoys hiking, watching horror movies, and practicing karate.

Research project title:
Learning the Regulariser for Inverse Problems

Supervisor(s):
Matthias Ehrhardt, Silvia Gazzola

Project description:
Solving inverse problems, such as those that arise in imaging applications, like computed tomography, is a challenging task due to their inherent ill-posedness and high dimensionality. Traditionally, one solves them using model-based methods, with variational regularisation models [2] being the most popular – where the choice of regulariser is usually a fixed, ad hoc decision. Recently, more data-driven approaches for determining regularisation operators and regularisation parameters have been considered [1]. This project is an exploratory study into these semi-data-driven methods for solving inverse problems, with a focus on the bi-level learning framework, and how one may use a neural network to learn, with mathematical guarantees, an appropriate regulariser.

[1] S. Arridge et al. “Solving inverse problems using data-driven models”. eng. In: Acta
numerica 28 (2019), pp. 1–174. issn: 0962-4929.
[2] J. Chung, S. Knepper, and J. G. Nagy. “Large-Scale Inverse Problems in Imaging”. eng. In:
Handbook of Mathematical Methods in Imaging. New York, NY: Springer New York, pp.
43–86. isbn: 0387929193.