Location: MIC-Arena, Maria-Goeppert-Str. 3, 23562 Lübeck
Title: "Inverse Problems with Errors in the Forward Operator and Applications in Deblurring"
We consider inverse problems where not only the data are noisy, but also the forward operator that can predict the data is not perfectly known. In this talk we discuss an approach to such problems that is based on the theory of partially ordered spaces - Banach lattices. A typical example of such an inverse problem is image deblurring, where the blurring kernel is not perfectly known. Failure to acknowledge the errors in the blurring kernel may lead to reconstruction artefacts that can be eliminated by modifying the reconstruction algorithms to account for errors in the operator. We discuss typical features of the partial-order-based approach in connection with total variation regularisation, such as loss of contrast, and show how the concept of debiasing on model manifolds can be used to overcome some of these issues.
This talk is based on a joint paper with Jan Lellmann (but also contains some new results).
