Variational regularisation for inverse problems with imperfect forward operators and general noise models. (30th November 2020) - Bungert, Leon; Burger, Martin; Korolev, Yury; Schönlieb, Carola-Bibiane
Abstract: We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and convex duality for general data fidelity terms and regularisation functionals. Both for a priori and a posteriori parameter choice rules, we obtain convergence rates of the regularised solutions in terms of Bregman distances. Our results apply to fidelity terms such as Wasserstein distances, φ -divergences, norms, as well as sums and infimal convolutions of those.