A Data-Driven Iteratively Regularized Landweber Iteration. (26th July 2020)

• Record Type: Journal Article
• Authors: Aspri, A.; Banert, S.; Öktem, O.; Scherzer, O.
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 10(2020)
• Page Start: 1190
• Page End: 1227
• Publication Date: 2020-07-26
• Subjects: Black box strategy -- expert and data driven regularization -- Iteratively regularized Landweber iteration; 65J20 -- 65J10 -- 65J15 -- 65J22; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1740734
• Languages: English
• ISSNs: 0163-0563

Abstract

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.