kth.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
A Data-Driven Iteratively Regularized Landweber Iteration
Johann Radon Institute Linz Austria.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-8110-6007
KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM. KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1118-6483
Johann Radon Institute Linz Austria.
2020 (English)In: Numerical Functional Analysis and Optimization, ISSN 0163-0563, E-ISSN 1532-2467Article in journal (Refereed) Published
Abstract [en]

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. 

Place, publisher, year, edition, pages
Taylor and Francis Inc. , 2020.
Keywords [en]
Black box strategy, expert and data driven regularization, Iteratively regularized Landweber iteration, Differential equations, Hilbert spaces, Inverse problems, Black boxes, Convergence and stability, Data driven, ILL-posed inverse problem, Landweber iteration, Linear inverse problems, Non-linear inverse problem, Numerical experiments, Iterative methods
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-274251DOI: 10.1080/01630563.2020.1740734ISI: 000524686300001Scopus ID: 2-s2.0-85082431265OAI: oai:DiVA.org:kth-274251DiVA, id: diva2:1452695
Note

QC 20200707

Available from: 2020-07-07 Created: 2020-07-07 Last updated: 2024-01-10Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopushttps://www.tandfonline.com/doi/abs/10.1080/01630563.2020.1740734?journalCode=lnfa20

Authority records

Banert, SebastianÖktem, Ozan

Search in DiVA

By author/editor
Banert, SebastianÖktem, Ozan
By organisation
Mathematics (Div.)Center for Industrial and Applied Mathematics, CIAM
In the same journal
Numerical Functional Analysis and Optimization
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 324 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf