(A gentle introduction to) Encoding prior knowledge in image- and data analysis

Energy-based method have become a popular tool for integrating prior knowledge in image and signal processing. In this talk, we will first give an
introduction to such techniques, focusing on variational models and non-smooth optimization. Many interesting energies are nonconvex, which complicates optimization. However, it is often possible to derive convex approximations which allow to find a good approximate minimizer. In the second part, we will discuss some recent results as well as applications including image restoration and reconstruction, segmentation, motion estimation, and processing of data on manifolds.