A Ginzburg-Landau- H^-1 Model and Its SAV Algorithm for Image Inpainting

Image inpainting models and the corresponding numerical algorithms play key roles in image processing. At present, the visual output of the oscillatory inpainting area is usually not natural. In this paper, we propose an image inpainting model based on the Ginzburg-Landau functional and H^-1 -norm. In the model, the H^-1 -fidelity term performs well in preserving the edges of the oscillatory inpainting areas, and the Ginzburg-Landau functional can provide additional geometric content. Theoretically, we prove the existence of the minimizer for the proposed energy functional. Based on the scalar auxiliary variable approach, we develop an efficient numerical scheme to solve the proposed model. Further, we use a time step adaptive strategy to accelerate the convergence. Experimental results validate the effectiveness of the proposed algorithm for image inpainting.