A Kaczmarz Version of the REGINN-Landweber Iteration for Ill-Posed Problems in Banach Spaces

In this work we present and analyze a Kaczmarz version of the iterative regularization scheme REGINN-Landweber for nonlinear ill-posed problems in Banach spaces [Jin, Inverse Problems 28(2012), 065002]. Kaczmarz methods are designed for problems which split into smaller subproblems which are then processed cyclically during each iteration step. Under standard assumptions on the Banach space and on the nonlinearity we prove stability and (norm-)convergence as the noise level tends to zero. Further, we test our scheme on the inverse problem of 2D electric impedance tomography not only to illustrate our theoretical findings but also to study the influence of different Banach spaces on the reconstructed conductivities.