A noise-level-free parameter-choice rule for iterated Lavrentiev regularization of nonlinear potential monotone ill-posed problems

We consider nonlinear ill-posed operator equations $F(x)=y$ in a Hilbert space, where $F$ is monotone with a Lipschitz continuous Fréchet derivative that is self-adjoint near the solution $x^\dg$ (a locally \emph{potential} operator), and only noisy data $y^δ$ with unknown noise norm $δ:=\|y-y^δ\|$