Abstract

When assigned with the task of reconstructing an image from given data the first challenge one faces is the derivation of a truthful image and data model. Such a model can be determined by the a-priori knowledge about the image, the data and their relation to each other. The source of this knowledge is either our understanding of the type of images we want to reconstruct and of the physics behind the acquisition of the data or we can thrive to learn parametric models from the data itself. The common question arises: how can we optimise our model choice? After a critical discussion of different image and data models we will turn towards deriving an optimal image reconstruction model using PDE constrained optimisation. In this framework we will consider optimal parameter derivation for total variation denoising with multiple noise distributions and optimising total generalised variation regularisation for its application in photography. Joint work with Luca Calatroni, Jan Lellmann, Juan Carlos De Los Reyes and Tuomo Valkonen.

http://www.maths.cam.ac.uk/postgrad/cca/oxbridgepde2014.html