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In this paper, we propose a fourth order PDE model for image inpainting basedon a variant of the famous Mumford-Shah (MS) image segmentation model.Convexity splitting is used to discrtised the time and we replace the Laplacianby its fractional counterpart in the time discretised scheme. Fourier spectralmethod is used for space discretization. Consistency, stability and convergenceof the time discretised model has been carried out. The model is tested on somestandard test images and compared them with the result of some models existedin the literature.

A Fractional Image Inpainting Model Using a Variant of Mumford-Shah Model