Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data (Q1944000)

The authors study Newton type methods generalizing the iteratively regularized Gauss-Newton method for nonlinear inverse problems. Convergence and convergence rates are established as the noise level tends to 0 both for an a priori stopping rule and for an a posteriori stopping rule. In particular, this general approach can cover inverse problems with the special case of Poisson data where the natural data misfit functional is given by the Kullback-Leibler divergence.