Regularisation methods of inverse problems: theory and computation

This project aims to investigate regularisation methods for inverse problems which are ill-posed in the sense that their solutions depend discontinuously on the data. When only noisy data is available, regularisation methods define stable approximate solutions by replacing the original inverse problem by a family of well-posed neighboring problems monitored by a so-called regularisation parameter. This project aims to develop purely data driven rules to choose the regularisation parameter and show how they work in theory and also in practice. It will also develop convex framework, acceleration strategies as well as preconditioning and splitting ideas to design efficient regularisation solvers.