Year: 2020
Type: article
Abstract: We derive and analyze a new variant of the iteratively regularized Landweber iteration, for solving linear and nonlinear ill-posed inverse problems. The method takes into account training data, which are used to estimate the interior of a black box, which is used to define the iteration process. We prove convergence and stability for the scheme in infinite dimensional Hilbert spaces. These theoretical results are complemented by some numerical experiments for solving linear inverse problems for the Radon transform and a nonlinear inverse problem for Schlieren tomography.
Authors: A. Aspri, S. Banert, O. Öktem, O. Scherzer
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3013097980