Generalizations of p-Laplace operator for image enhancement: Part 2 - Baravdish, George; Cheng, Yuanji; Svensson, Olof; Åström, Freddie (Communications on pure and applied analysis, 2020)
We have in a previous study introduced a novel elliptic operator \begin{document}$ Δ_{(p, q)} u = |\nabla u|^qΔ_1 u +(p-1)|\nabla u|^{p-2} Δ_{∞} u $\end{document} , \begin{document}$ p \ge 1 $\end{document} , \begin{document}$ q\ge 0, $\end{document} as a generalization of the \begin{document}$ p $\end{document} -Laplace operator. In this paper, we establish the well-posedness of the parabolic equation \begin{document}$ u_{t} = |\nabla u|^{1-q}Δ_{(1+q, q)}, $\end{document} where \begin{document}$ q = q(|\nabla u|) $\end{document} is continuous and has range in \begin{document}$ [0, 1], $\end{document} 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.
Gesehen am 02.06.2020