Mohammad Sadegh graduated from the PSL- Dauphine university in 2021 with an MSc in Applied and Theoretical Mathematics after completing a BSc in Mathematics and Applications from the University of Tehran. After getting familiar with a variety of courses in fundamental aspects of mathematics, his main interest appeared in mathematical optimization and numerical analysis. During his MSc in Paris, he expanded his knowledge about PDEs and variational methods. His master’s thesis was about alternating projection methods, some accelerations on them, and an algorithm for an optimal transport problem. Outside of mathematics, he loves watching and playing football, listening to music, singing Iranian music, watching movies, and drinking coffee. Moreover, he is into technology and likes the mathematical aspects of machine learning.

Research project title:
Bilevel Learning

Supervisor(s):
Matthias Ehrhardt, Subhadip Mukherjee

Project description:
Inverse problems are the process of estimating parameters of interest from indirect, potentially noisy, measurements. They are ubiquitous in many areas of science and engineering, including virtually every modern medical imaging modality. The standard approach to inverse problems and specifically image reconstruction is variational regularisation. Although hugely successful, typically, it is dependent on a range of parameters that have to be set manually. State-of-the-art image reconstruction methods learn these parameters from training data using a variety of machine learning techniques, such as bilevel methods. Bilevel learning can be seen as a method to learn parameters best suited to a specific task. From the mathematical point of view, this strategy leads to a nested optimisation problem which is computationally very difficult to handle. This PhD project lies in algorithms for bilevel learning used in the mathematical imaging literature. In particular, derivative-free and first-order methods tailored for the mentioned type of problems and their challenges are investigated, as well as their convergence theorems. Alongside these algorithms the usage of data-adaptive input-convex neural networks as the regulariser, will be explored. Applications of this PhD project include undersampled MRI reconstruction; image denoising, deblurring and segmentation; and data clustering. Also, other sorts of applications in the general category of supervised learning are desirable.