Student
Amin Sabir

Amin graduated with an MSci Mathematics degree from UCL in 2022

Amin graduated with an MSci Mathematics degree from UCL in 2022, where he developed a keen interest into asymptotics, fluid dynamics and stochastic processes. For his Masters project, Amin delved in depth into asymptotics and hyperasymptotics with their roles in solving ODEs like the Airy equation. He has also done some group projects including using ML techniques to determine different price ranges for a smartphone dataset and helped implement a Python mathematical model for oxygen saturation, contributing to a published paper on the effects of Hypoxia.

When not doing maths, Amin loves to do long distance running which included participating in the London Marathon, half marathons and the weekly parkuns!

Research project title:
Data-driven regularisation methods for inverse problems

Supervisor(s):
Yury Korolev and Matthias Ehrhardt

Project description: 
In inverse problems, such as computed tomography (CT) and photoacoustic tomography (PAT), the goal is to reconstruct a quantity of interest from indirect and often noisy measurements. These problems are challenging due to their ill-posed nature and the complexity of the data. Traditional approaches, like variational regularisation, have been effective, but are often limited by their handcrafted design (e.g. promoting smoothness in the reconstruction), which can be restrictive and insufficiently adaptive for capturing diverse reconstruction features.

Recently, data-driven regularisation methods, such as plug-and-play (PnP), have been introduced to integrate learned priors from training data. These methods are designed to address a wider range of inverse problems, including tasks like image denoising and deblurring. This project will explore the application of such data-driven approaches to medical imaging, focusing on their theoretical foundations, practical implementation, and mathematical guarantees. The goal is to understand the inner workings of these methods and identify the most suitable regularisation techniques for specific inverse problem settings in medical imaging.