THE FRACTIONAL LAPLACIAN BASED IMAGE INPAINTING

Image inpainting is the process of repairing damaged or missing areas of an image by utilizing information from its surrounding environment. The fractional order operator, which processes image details like textures and edges with a finer scale, has demonstrated better outcomes and success in im-age processing. This study draws inspiration from the definition of singular integral of the fractional Laplacian and presents two adaptive variational func-tionals for image inpainting, showcasing a stable variational scheme. Moreover, the numerical discretisation scheme used for the derived fractional Laplacian PDEs was constructed. The proposed models can simultaneously restore miss-ing, corrupted, or undesirable regions while removing noise. Numerical exper-iments were conducted to test the image inpainting techniques, accompanied by method comparisons.