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Extension of p-Laplace Operator for Image Denoising
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
Malmö University, Malmö, Sweden.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-3324-2298
Heidelberg Collaboratory for Image Processing, Heidelberg University, Heidelberg, Germany.
2016 (English)In: 27th IFIP TC 7 Conference, CSMO 2015, Sophia Antipolis, France, June 29 - July 3, 2015, Revised Selected Papers / [ed] Bociu, Lorena; Désidéri, Jean-Antoine; Habbal, Abderrahmane, Springer, 2016, p. 107-116Chapter in book (Refereed)
Abstract [en]

In this work we introduce a novel operator $$\displaystyle \varDelta _(p,q)$$ as an extended family of operators that generalize the p-Laplace operator. The operator is derived with an emphasis on image processing applications, and particularly, with a focus on image denoising applications. We propose a non-linear transition function, coupling p and q, which yields a non-linear filtering scheme analogous to adaptive spatially dependent total variation and linear filtering. Well-posedness of the final parabolic PDE is established via pertubation theory and connection to classical results in functional analysis. Numerical results demonstrates the applicability of the novel operator $$\displaystyle \varDelta _(p,q)$$ .

Place, publisher, year, edition, pages
Springer, 2016. p. 107-116
Series
Advances in Information and Communication Technology, ISSN 1868-4238, E-ISSN 1868-422X
Keyword [en]
p-Laplace operator, Parabolic equations, Image denoising, Anisotropic diffusion, Inverse problems
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-140918DOI: 10.1007/978-3-319-55795-3_9Scopus ID: 2-s2.0-85018676931ISBN: 9783319557946 (print)ISBN: 9783319557953 (electronic)OAI: oai:DiVA.org:liu-140918DiVA: diva2:1141712
Available from: 2017-09-15 Created: 2017-09-15 Last updated: 2017-09-20Bibliographically approved

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Svensson, Olof

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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Language
  • de-DE
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  • en-US
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  • nn-NB
  • sv-SE
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Output format
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