Heuristic rule for non-stationary iterated Tikhonov regularization in Banach spaces

Abstract

In this paper we propose a heuristic rule of Hanke–Raus type for non-stationary iterated Tikhonov regularization for solving ill-posed inverse problems in Banach spaces. This heuristic rule does not need any information on the noise level and is fully data driven. Under certain conditions on the noisy data, we obtain a convergence result. Various numerical simulations are provided to illustrate the efficiency of the proposed heuristic rule.