# Exact solutions to the one dimensional TGV regularisation problem

2014-02-07

Presenter: Konstantinos Papafitsoros (University of Cambridge)

Co-author: Kristian Bredies (University of Graz)

### Abstract

Total generalised variation (TGV) is a recently introduced, high quality regulariser which has successfully used in many applications of mathematical imaging. It tends to preserve not only edges but also smooth structures, thus avoiding the staircasing effect, a well known artifact of total variation regularisation. We provide exact solutions to the one dimensional TGV problem with $L^{2}$ fidelity term, using simple piecewise affine functions as data terms. This gives a further insight into the behaviour of the solutions with respect to the TGV parameters and more generally into the regularising mechanisms of TGV.