This course will provide an introduction to some basic mathematical problems in image formation and image reconstruction. In addition to modelling forward problems, we consider classical regularization strategies, ensuring well-posedness of the image reconstruction problems. Beyond this classical setting, we dive into modern deep-learning methods, which allow solving inverse problems in a data-dependent approach. Finally, we also consider uncertainty quantification, where we employ the Bayesian view point of inverse problems.
Analysis, Linear Algebra, Basic Numerical Analysis and some programming skills
Mueller, J. L., & Siltanen, S. (Eds.). (2012). Linear and nonlinear inverse problems with practical applications. Society for Industrial and Applied Mathematics.
Natterer, F., & Wübbeling, F. (2001). Mathematical methods in image reconstruction. Society for Industrial and Applied Mathematics.