EU Regional School - Burger Seminar
Prof. Dr. Burger - Variational Image Reconstruction
University of Münster
Imaging has become a ubiqituous technique in modern science and our daily lives, even leading to the development of the interdisciplinary field of "Image Science", in which mathematics plays a key role. The first crucial mathematical task is image reconstruction from indirect measurements, which is often a challening ill-posed inverse problem. In this lecture we discuss the solution of image reconstruction problems by modern variational methods, in particular using singular regularization energies such as total variation and extensions. We explain how such methods can effectively take into account the physics and statistical properties of the image generation process as well as incorporate prior knowledge about the images. We further discuss computational methods and applications in biomedicine, as well as some approaches and challenges in dynamic imaging.