Krylov methods are well-known and efficient iterative solvers for linear systems of equations, and they are often employed as iterative regularization methods for linear inverse problems. Krylov methods are well-suited for imaging problems. In this talk we will explore classical Krylov methods when applied to solve Tikhonov-like regularized problems, and introduce new flexible Krylov methods that allow to efficiently incorporate nonnegativity constraints and 1-norm penalization terms within the solution process.

This presentation is part of Minisymposium “MS59 - Approaches for fast optimisation in imaging and inverse problems (3 parts)”
organized by: Jingwei Liang (University of Cambridge) , Carola-Bibiane Schönlieb (University of Cambridge) , Mila Nikolova (CMLA - CNRS ENS Cachan, University Paris-Saclay) .

Authors:

Silvia Gazzola (University of Bath)

Keywords:

computed tomography, image deblurring, image reconstruction, numerical linear algebra