Variational regularisation for inverse problems with imperfect forward operators and general noise models
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.
H2020 Marie Skłodowska-Curie Actions (691070 CHiPS 777826 (NoMADS))
Engineering and Physical Sciences Research Council (EP/N014588/1 EP/S026045/1 EP/T003553/1 EP/V003615/1)
Leverhulme Trust (Breaking the non-convexity barrier Philip Leverhulme Prize)
Wellcome Trust (Wellcome Innovator Award RG98755)
Royal Society (NF170045)