Abstract:

Inverse problems are concerned with the reconstruction of the quantity of interest, such as a medical image, from indirectly measured, and typically noisy, data. The relationship between the quantities of interest and the data is modelled using a so-called forward operator, which is the mathematical model of the data acquisition process. In practice, not only the data are noisy, but also the forward operator is often not perfectly known as it may involve imperfect calibration measurements or simplified models. Neglecting these imperfections and using an erroneous forward operator may have severe consequences and render the inversion ill-posed. In this talk I will present an approach to inverse problems with imperfect forward models that relies on partially ordered spaces, particularly focusing on image deblurring with errors in the blurring kernel. I will discuss convergence rates for regularised solutions of such problems and show that they coincide with known convergence rates for problems with exact operators under some reasonable assumptions. This is joint work with Martin Burger and Julian Rasch.