Fast Iterative Regularisation Methods

: (Alternative Format Thesis)

Abstract

This thesis assembles three published papers containing original research in the area of regularization techniques for large-scale linear discrete inverse problems. These include a new principled algorithmic framework for Krylov-Tikhonov methods that automatically sets the regularization parameter, and new algorithms for $\ell_1$-$\ell_p$ and total variation regularization. In order to present the natural framework of this thesis, a general introduction to large scale linear discrete inverse problems is given first, along with a brief description of the nature of these problems that motivates the need for regularization.