Martin Burger: Variational Methods for Image Reconstruction from Photon Counts

The improvement of imaging techniques in the last decades nowadays allow to investigate novel challenges in biomedicine. E.g. improvements in PET allow to study pharmacokinetics and physiological processes dynamically and in a quantitative manner. Improvements in fluorescence microscopy towards time-resolved imaging or towards high resolution (e.g. nanoscopy) allow novel insights into cellular and intracellular processes. The downside of this development is that image quality has to be sacrificed to a certain extent, in particular one has to deal with low photon counts (due to decreased spatial size or time windows).  This talk will present several variational methods to deal with this situation in image reconstruction and image deconvolution. The main ingredients are appropriate stochastic modelling of the noise and Bayesian MAP estimation based on edge-preserving priors. In order to cure systematic errors of MAP estimates, in particular severe loss of contrast that can easily lead to missing small structures, we introduce inverse scale space methods and sketch their main properties. We present applications to dynamic PET, intravital and stimulated emission depletion (STED) microscopy.