Generalizations of p-Laplace operator for image enhancement

• Verfasst von: Baravdish, George [VerfasserIn]
• Verfasst von: Cheng, Yuanji [VerfasserIn]
• Verfasst von: Svensson, Olof [VerfasserIn]
• Verfasst von: Åström, Freddie [VerfasserIn]
• Titel: Generalizations of p-Laplace operator for image enhancement
• Titelzusatz: Part 2
• Verf.angabe: George Baravdish, Yuanji Cheng, Olof Svensson, and Freddie Åström
• E-Jahr: 2020
• Jahr: July 2020
• Umfang: 23 S.
• Fussnoten: Gesehen am 02.06.2020
• Titel Quelle: Enthalten in: Communications on pure and applied analysis
• Ort Quelle: Springfield, Mo. : AIMS, 2002
• Jahr Quelle: 2020
• Band/Heft Quelle: 19(2020), 7, Seite 3477-3500
• ISSN Quelle: 1534-0392
• DOI: doi:10.3934/cpaa.2020152
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1699151539

Abstract

<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>