Abstract
Image inpainting is used to restore some damaged or missing information regions of an image based on the surrounding information. Inspired by the fourth-order partial differential equation (PDE), this study presents two adaptive variational functionals for image inpainting, shows a stable variational scheme and investigates existence and uniqueness of solution for the minimising functionals. A consistent numerical discretisation scheme is also constructed for the derived fourth-order PDEs. The proposed models can simultaneously restore the missing, corrupted or undesirable regions and remove noise. Some successful image inpainting experiments and method comparisons are also provided in this study.
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