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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 444, Pages 47–88 (Mi znsl6268)  
This article is cited in 1 scientific paper (total in 1 paper)

An alternative approach towards the higher order denoising of images. Analytical aspects

M. Bildhauer, M. Fuchs, J. Weickert

Universität des Saarlandes, D-66041 Saarbrücken, Germany
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Abstract: We investigate theoretical aspects of a variational model for the denoising of images which can be interpreted as a substitute for a higher order approach. In this model, the smoothness term that usually involves the highest derivatives is replaced by a mixed expression for a second unknown function in which only derivatives of lower order occur. Our main results concern existence and uniqueness as well as the regularity properties of the solutions to this variational problem established under various assumptions imposed on the growth rates of the different parts of the energy functional.
Bibliography: 56 titles.
Key words and phrases: image restoration, variational approach, higher order denoising.
Received: 18.01.2016
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 224, Issue 3, Pages 414–441
DOI: https://doi.org/10.1007/s10958-017-3425-1
Bibliographic databases:
Document Type: Article
UDC: 517
Language: English
Citation: M. Bildhauer, M. Fuchs, J. Weickert, “An alternative approach towards the higher order denoising of images. Analytical aspects”, Boundary-value problems of mathematical physics and related problems of function theory. Part 45, Zap. Nauchn. Sem. POMI, 444, POMI, St. Petersburg, 2016, 47–88; J. Math. Sci. (N. Y.), 224:3 (2017), 414–441
Citation in format AMSBIB
\Bibitem{BilFucWei16}
\by M.~Bildhauer, M.~Fuchs, J.~Weickert
\paper An alternative approach towards the higher order denoising of images. Analytical aspects
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~45
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 444
\pages 47--88
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6268}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3509677}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 224
\issue 3
\pages 414--441
\crossref{https://doi.org/10.1007/s10958-017-3425-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85020222474}
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  • https://www.mathnet.ru/eng/znsl/v444/p47
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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