Fractional $ 1 $-Laplacian evolution equations to remove multiplicative noise

<p style='text-indent:20px;'>In this paper, we propose a new image denosing model to remove the multiplicative noise by a maximum a posteriori estimation and an inhomogeneous fractional <inline-formula><tex-math id="M2">\begin{document}$ 1 $\end{document}</tex-math></inline-formula>-Laplace evolution equation. The main difficulty of the problem is the equation will become very singular when <inline-formula><tex-math id="M3">\begin{document}$ u(x) = u(y) $\end{document}</tex-math></inline-formula>. The existence and uniqueness of the weak positive solution are proved. Numerical examples demonstrate the better capability of our model on some heavy multiplicative noised images.</p>