A projected Bouligand–Landweber iteration for non-smooth ill-posed problems

Abstract

In this work, we formulate a projected Bouligand–Landweber iteration for non-smooth ill-posed problems. The approach is a combination of Bouligand–Landweber iteration and the projection onto stripes the width of which is controlled by both the noise level and the structure of the operator. Since the forward mapping is not Fréchet differentiable, the convergence analysis will be based on the concept of asymptotic stability and a generalized tangential cone condition. Finally, numerical examples will be presented.