Lavrentiev's regularization method in Hilbert spaces revisited
Provides theoretical convergence rate results for Lavrentiev regularization, which is relevant for researchers working on inverse problems and regularization theory.
The paper revisits Lavrentiev's regularization method for nonlinear ill-posed problems with monotone operators in Hilbert spaces, deriving new convergence rates under novel variational source conditions and approximate source conditions.
In this paper, we deal with nonlinear ill-posed problems involving monotone operators and consider Lavrentiev's regularization method. This approach, in contrast to Tikhonov's regularization method, does not make use of the adjoint of the derivative. There are plenty of qualitative and quantitative convergence results in the literature, both in Hilbert and Banach spaces. Our aim here is mainly to contribute to convergence rates results in Hilbert spaces based on some types of error estimates derived under various source conditions and to interpret them in some settings. In particular, we propose and investigate new variational source conditions adapted to these Lavrentiev-type techniques. Another focus of this paper is to exploit the concept of approximate source conditions.