Abstract

In this talk, we recap the framework of Bounded Variation functions and their main features relevant to Imaging. In the course of that discussion we highlight some drawbacks of TV reconstruction and introduce higher-order versions of TV which improve upon them, highlighting the numerical obstacles arising when solving such models and possible directions (such as ADI directional splitting schemes).

The rest of talk will focus on my current research on the optimal setup of these models by means a nonlinear PDE constrained optimisation, based on a training set of original and noisy images. In such approach, the optimal weights are computed such that the corresponding total variation regularised solutions (encoded in the constraints) ‘best’ fit the original images. To improve upon the efficiency of the numerical solvers, we use dynamical sampling schemes to compute the optimal parameters.

This is a joint work with J. C. De Los Reyes and C.-B. Schönlieb.