An iterative regularization method for nonlinear problems based on Bregman projections

In this paper, we present an iterative method for the regularization of ill-posed, nonlinear problems. The approach is based on the Bregman projection onto stripes the width of which is controlled by both the noise level and the structure of the operator. In our investigations, we follow (Lorenz et al 2014 SIAM J. Imaging Sci. 7 1237–62) and extend the respective method to the setting of nonlinear operators. Furthermore, we present a proof for the regularizing properties of the method. (paper)