Dr. Frank Bauer: Research and Development in Applied Mathematics
 Subjects of Research
   
 
Inverse problems and paramter choice strategies
Ill-posed (or inverse) problems are occuring in numerous real situations. Almost everytime when we measure data by a kind of averaging process (which is an easy forward problem) the inversion, namely recovering the original information out of the measured data is extremely unstable. Examples for such problems are
If we used a naive inversion procedure the error in the high frequency compentents would get extremely amplified, the solution has nothing to do with the original information. Therefore one needs to damp this high frequency part, despite that one also looses the high frequency components in the solution, i.e. makes by purpose some small error in order to avoid a large one. This procedure is called regularization, how much one damps down these high frequency components is associated with the regularization parameter. Choosing this parameter in an optimal way is crucial.
Image Processing
Image processing is a part of computer science and mathematics which is getting increasingly important in technical applications and industry for automatization and quality control. Particular examples are As the occuring data sets are rather big and the applications highly sensitive, the underlying algorithms need to be fast and reliable.