On convergence rates for iteratively regularized Newton-type methods under a Lipschitz-type nonlinearity condition

Abstract

Abstract We investigate a generalization of the well-known iteratively regularized Gauss–Newton method where the Newton equations are regularized variationally using general data fidelity and penalty terms. To obtain convergence rates, we use a general error assumption which has recently been shown to be useful for impulsive and Poisson noise. We restrict the nonlinearity of the forward operator only by a Lipschitz-type condition and compare our results to other convergence rates results proven in the literature. Finally we explicitly state our convergence rates for the aforementioned case of Poisson noise to shed some light on the structure of the posed error assumption.