FSI Schemes: Fast Semi-Iterative Solvers for PDEs and Optimisation MethodsMS59

We introduce a simple and highly efficient acceleration strategy, for accelerating methods like projected gradient descent method, which leads to so-called Fast Semi-Iterative schemes that extrapolate the basic solver iteration with the previous iterate. To derive suitable extrapolation parameters, we establish a recursion relation that connects box filtering with an explicit scheme for 1D homogeneous diffusion. Our experiments show their benefits for anisotropic diffusion inpainting, nonsmooth regularisation, and Nesterov’s worst case problems.

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) .

Joachim Weickert (Saarland University)