Before revision:  These monotonicity methods build the basis for the improvement of the ] standard one-step linearization method.
After revision:  These monotonicity methods build the basis for the improvement of the ], but have no rigorously proven convergence theory. Therefore we show how the monotonicity methods can be converted into a regularization method for a data-fitting functional without losing the convergence properties of the monotonicity methods. This is a great advantage and a significant improvement over standard one-step linearization method.