An accelerated Homotopy-Perturbation-Kaczmarz method for solving nonlinear inverse problems

In this paper, we propose an accelerated homotopy-perturbation-Kaczmarz iteration based on sequential subspace optimization method for solving nonlinear systems of inverse problems. The method is to iteratively project the initial value onto stripes the width of which are controlled by the search direction, the forward operator and the noise level to expedite the convergence. Under some general assumptions, we provide the convergence and regularization analysis for the proposed method. Finally, two numerical examples on inverse potential problems are presented to illustrate the effectiveness of reconstructing the solution and acceleration effect of the method.