Current Research Activities
Our research is focused on theory and applications of inverse problems. An inverse problem means the computation of a quantity from a parameter space, which is not directly oservable, from measured data that contain information about the searched quantity. A mathematical model, which usually is represented by an operator equation or recently also by a neural network, describes the connection between the parameter and the data space. The reconstruction process then consists by a stable inversion procedure that maps the given data to the searched quantity. Usually inverse problems are illposed what means that even small data errors deteriorate the inversion process leading to a useless solution. This is why stable solution schemes have to be developed, so called regularization methods. In our research we follow all the way from mathematical modeling, analysis of the underlying mathematical operator, development of problem adapted regularization methods down to the implementation and validation of these methods using innovative numerical solvers. Our fundamental research is currently focused at regularization methods in Banach and Bochner spaces, where the latter play a prominent role in the emerging field of dynamic inverse problems, where we consider applications with timedependent data to compute timedependent parameters. Applications are
