Semi-Heuristic Parameter Choice Rules for Tikhonov Regularisation with Operator Perturbations

We study the choice of the regularisation parameter for linear ill-posed problems in the presence of data noise and operator perturbations, for which a bound on the operator error is known but the data noise-level is unknown. We introduce a new family of semi-heuristic parameter choice rules that can be used in the stated scenario. We prove convergence of the new rules and provide numerical experiments that indicate an improvement compared to standard heuristic rules.