The two-point gradient methods for nonlinear inverse problems based on Bregman projections

In this paper, we propose and analyze a projected two-point gradient method for solving nonlinear inverse 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, and the two-point gradient method is efficient for acceleration. The method allows to use $L^1-$liked penalty terms, which is significant in sparsity reconstructions. We present a proof for the regularizing properties of the method, some parameter identification examples are presented to illustrate the effectiveness of the proposed method.