TITLE: Total variation in imaging: theory, models, examples and challenges
SPEAKER: Luca Calatroni (Cambridge Centre for Analysis, University of Cambridge)

ABSTRACT:

The use of Total Variation in Imaging has become extremely popular and well-known due to its capability of preserving structures, e.g. edges in images. In this talk, we recap the framework  of Bounded Variation functions and their main features relevant to Imaging, considering as an example the well-known Rudin Osher Fatemi (ROF) denoising model. Further, we discuss other challenging imaging problems like deblurring, inpainting and image segmentation. In the course of that discussion we highlight some drawbacks of TV reconstruction and introduce higher-order versions of TV which improve upon them. These models are challenging both from an analytical and a numerical point of view due to the non-smoothness of solutions and the presence of higher order derivatives. In this talk I will present some possible numerical strategies (ADI splitting schemes and primal-dual formulations with penalty terms) that render the problem computationally tractable. We conclude the talk presenting my current research on the optimal setup of these models by means a nonlinear PDE constrained optimisation.