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.

A Data-Driven Iteratively Regularized Landweber Iteration / A. Aspri, S. Banert, O. Oktem, O. Scherzer. - In: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION. - ISSN 0163-0563. - 41:10(2020), pp. 1190-1227. [10.1080/01630563.2020.1740734]

A Data-Driven Iteratively Regularized Landweber Iteration

A. Aspri
Primo
;
2020

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.
Black box strategy; expert and data driven regularization; Iteratively regularized Landweber iteration
Settore MAT/08 - Analisi Numerica
Settore MAT/05 - Analisi Matematica
Article (author)
File in questo prodotto:
File Dimensione Formato  
6.Aspri_NFAO20.pdf

accesso riservato

Descrizione: Articolo principale
Tipologia: Publisher's version/PDF
Dimensione 1.1 MB
Formato Adobe PDF
1.1 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/898380
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact