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

This paper deals with a class of fractional 1-Laplacian diffusion equations with variable orders, proposed as a model for removing multiplicative noise in images. The well-posedness of weak solutions to the proposed model is proved. To overcome the essential difficulties encountered in the approximation process, we place particular emphasis on studying the density properties of the variable-order fractional Sobolev spaces. Numerical experiments demonstrate that our model exhibits favorable performance across the entire image.