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An optimal regularization method for convolution equations on the sourcewise represented set
Örebro University, School of Science and Technology, Örebro University, Sweden. (Mathematics)ORCID iD: 0000-0003-4023-6352
Department of Mathematics, Faculty of Physics, M. V. Lomonosov Moscow State University, Leninskie Gory, Moscow, Russian Federation.
Department of Mathematics, Faculty of Physics, M. V. Lomonosov Moscow State University.
2015 (English)In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 23, no 5, 465-475 p.Article in journal (Refereed) Published
Abstract [en]

In this article, we consider an inverse problem for the integral equation of the convolution typein a multidimensional case. This problem is severely ill-posed. To deal with this problem, using a prioriinformation (sourcewise representation) based on optimal recovery theory we propose a new method. Theregularization and optimization properties of this method are proved. An optimal minimal a priori error ofthe problem is found. Moreover, a so-called optimal regularized approximate solution and its correspondingerror estimation are considered. Eciency and applicability of this method are demonstrated in a numericalexample of the image deblurring problem with noisy data.

Place, publisher, year, edition, pages
Berlin, Germany: Walter de Gruyter, 2015. Vol. 23, no 5, 465-475 p.
Keyword [en]
Inverse problem, convolution, regularization method, optimal recovery, error estimation, Fourier transform
National Category
Mathematical Analysis Other Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-47926DOI: 10.1515/jiip-2014-0047ISI: 000362193500004Scopus ID: 2-s2.0-84943642498OAI: oai:DiVA.org:oru-47926DiVA: diva2:900413
Note

Funding Agency:

RFBR 14-01-00182-a  14-01-91151-NSFC-a

Available from: 2016-02-04 Created: 2016-02-04 Last updated: 2016-02-09Bibliographically approved

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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • harvard1
  • 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