Generalizations of p-Laplace operator for image enhancement: Part 2
<p style='text-indent:20px;'>We have in a previous study introduced a novel elliptic operator <inline-formula><tex-math id="M2">\begin{document}$ \Delta_{(p, q)} u = |\nabla u|^q\Delta_1 u +(p-1)|\nabla u|^{p-2} \Delta_{\infty} u $\end{document}</tex-math>...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
July 2020
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| In: |
Communications on pure and applied analysis
Year: 2020, Volume: 19, Issue: 7, Pages: 3477-3500 |
| ISSN: | 1553-5258 |
| DOI: | 10.3934/cpaa.2020152 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.3934/cpaa.2020152 Verlag, lizenzpflichtig, Volltext: https://www.aimsciences.org/article/doi/10.3934/cpaa.2020152 
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| Author Notes: | George Baravdish, Yuanji Cheng, Olof Svensson, and Freddie Åström |
| Summary: | <p style='text-indent:20px;'>We have in a previous study introduced a novel elliptic operator <inline-formula><tex-math id="M2">\begin{document}$ \Delta_{(p, q)} u = |\nabla u|^q\Delta_1 u +(p-1)|\nabla u|^{p-2} \Delta_{\infty} u $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M3">\begin{document}$ p \ge 1 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M4">\begin{document}$ q\ge 0, $\end{document}</tex-math></inline-formula> as a generalization of the <inline-formula><tex-math id="M5">\begin{document}$ p $\end{document}</tex-math></inline-formula>-Laplace operator. In this paper, we establish the well-posedness of the parabolic equation <inline-formula><tex-math id="M6">\begin{document}$ u_{t} = |\nabla u|^{1-q}\Delta_{(1+q, q)}, $\end{document}</tex-math></inline-formula> where <inline-formula><tex-math id="M7">\begin{document}$ q = q(|\nabla u|) $\end{document}</tex-math></inline-formula> is continuous and has range in <inline-formula><tex-math id="M8">\begin{document}$ [0, 1], $\end{document}</tex-math></inline-formula> in the framework of viscosity solutions. We prove the consistency and convergence of the numerical scheme of finite differences of this parabolic equation. Numerical simulations shows the advantage of this operator applied to image enhancement.</p> |
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| Item Description: | Gesehen am 02.06.2020 |
| Physical Description: | Online Resource |
| ISSN: | 1553-5258 |
| DOI: | 10.3934/cpaa.2020152 |