Variable-order fractional 1-Laplacian diffusion equations for multiplicative noise removal

Abstract

In this paper, we study a class of fractional $1$-Laplacian diffusion equations with variable orders, proposed as a model for multiplicative noise removal. The existence and uniqueness of the weak solution are proven. To overcome the difficulties in the approximation process,we place particular emphasis on studying the density propertiesof the variable-order fractional Sobolev spaces. Numerical experiments demonstrate that our model exhibits favorable performance across the entire image.

arXiv comment28 pages, 6 figures

References in corpus (3)

• Fractional Quantum Mechanics and Levy Path Integrals
• Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents
• Evolution problems of Leray-Lions type with nonhomogeneous Neumann boundary conditions in metric random walk spaces