The residual method consists in minimizing a regularization functional over a feasible set defined by fidelity constraints. These fidelity constraints can account for errors in the forward operator, however, in the classical setting in normed spaces, this results in a non-convex optimization problem. In partially ordered spaces fidelity constraints can be expressed in a way that yields convex feasible sets. We will present the theory and applications in deblurring with uncertainty in the blurring kernel.

This presentation is part of Minisymposium “MS72 - Inverse problems with imperfect forward models (2 parts)”
organized by: Yury Korolev (University of Cambridge) , Martin Burger (University of Muenster) .

Authors:

Yury Korolev (University of Cambridge)

Martin Burger (University of Muenster)

Keywords:

image deblurring, image reconstruction, inverse problems