Variational regularisation for inverse problems with imperfect forward operators and general noise models

Funder: Cantab Capital Institute for the Mathematics of InformationFunder: National Physical Laboratory; doi: https://doi.org/10.13039/501100007851Funder: Alan Turing Institute; doi: https://doi.org/10.13039/100012338Abstract: 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