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A Ginzburg-Landau-\({H}^{-1}\) Model and Its SAV Algorithm for Image Inpainting

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Abstract

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.

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Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

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Acknowledgements

This work is partially supported by the Fundamental Research Fund for the Central Universities (HIT. NSRIF202202), the National Natural Science Foundation of China (12171123, 11971131, 11871133, 11671111, U1637208, 61873071, 51476047). The Natural Science Foundation of Heilongjiang Province of China (LH2021A011) and China Postdoctoral Science Foundation (2020M670893). China Society of Industrial and Applied Mathematics Young Women Applied Mathematics Support Research Project.

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Authors and Affiliations

  1. School of Mathematics, Harbin Institute of Technology, Harbin, China

    Xiangyu Bai, Jiebao Sun, Wenjuan Yao & Zhichang Guo

  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Jie Shen

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  1. Xiangyu Bai
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Bai, X., Sun, J., Shen, J. et al. A Ginzburg-Landau-\({H}^{-1}\) Model and Its SAV Algorithm for Image Inpainting. J Sci Comput 96, 40 (2023). https://doi.org/10.1007/s10915-023-02252-z

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