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It is a challenging task to prevent the staircase effect and simultaneously preserve sharp edges in image inpainting. For this purpose, we present a novel nonconvex extension model that closely incorporates the advantages of total generalized variation and edge-enhancing nonconvex penalties. This improvement contributes to achieve the more natural restoration that exhibits smooth transitions without penalizing fine details. To efficiently seek the optimal solution of the resulting variational model, we develop a fast primal-dual method by combining the iteratively reweighted algorithm. Several experimental results, with respect to visual effects and restoration accuracy, show the excellent image inpainting performance of our proposed strategy over the existing powerful competitors.

Nonconvex Total Generalized Variation Model for Image Inpainting