Preprint D115/2014
A Kaczmarz version of the REGINN-Landweber iteration for ill-posed problems in Banach spaces
Antonio Leitao | Fabio Margotti | Andreas Rieder

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 [Q. 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 two dimensional electric impedance tomography not only to illustrate our theoretical findings

but also to study the influence of different Banach spaces on the reconstructed conductivities.