Volume 57, pp. 216-241, 2022.

A numerical comparison of some heuristic stopping rules for nonlinear Landweber iteration

Simon Hubmer, Ekaterina Sherina, Stefan Kindermann, and Kemal Raik


The choice of a suitable regularization parameter is an important part of most regularization methods for inverse problems. In the absence of reliable estimates of the noise level, heuristic parameter choice rules can be used to accomplish this task. While they are already fairly well understood and tested in the case of linear problems, not much is known about their behaviour for nonlinear problems and even less in the respective case of iterative regularization. Hence, in this paper, we numerically study the performance of some of these rules when used to determine a stopping index for Landweber iteration for various nonlinear inverse problems. These are chosen from different practically relevant fields such as integral equations, parameter estimation, and tomography.

Full Text (PDF) [2.1 MB], BibTeX

Key words

heuristic parameter choice rules, Landweber iteration, inverse and ill-posed problems, nonlinear operator equations, numerical comparison

AMS subject classifications

65J20, 65F22, 47J06, 35R25

Links to the cited ETNA articles

[51]Vol. 38 (2011), pp. 233-257 Stefan Kindermann: Convergence analysis of minimization-based noise level-free parameter choice rules for linear ill-posed problems
[52]Vol. 40 (2013), pp. 58-81 Stefan Kindermann: Discretization independent convergence rates for noise level-free parameter choice rules for the regularization of ill-conditioned problems
[54]Vol. 57 (2022), pp. 17-34 Stefan Kindermann: On the tangential cone condition for electrical impedance tomography
[59]Vol. 53 (2020), pp. 217-238 Stefan Kindermann and Kemal Raik: A simplified L-curve method as error estimator

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