Caputo fractional-time of a modified Cahn-Hilliard equation for the inpainting of binary images

In this work, we present a new version of the Cahn-Hilliard equation to deal with binary image inpainting. The proposed model is unique due to its memory effect ability implemented by the time fractional derivative. Also, this model has a new diffusion term that gives a topological reconnection and a well sharpness of edges and corners. We give an existence result with some numerical tests implemented by the convexity splitting to show the efficiency of the proposed model.

Keywords:

Image inpainting , Cahn-Hilliard equation , time-fractional , Caputo derivative , finite difference , convexity splitting