Application of Fractional Laplacian Partial Differential Equation in Mural Image Inpainting

Ayiman Dawuken; Gulijiamali Maimaitiaili; Askar Rozi; Abdujelil Abdurahman

doi:10.53941/cssc.2026.100005

Abstract

The application of a variational partial differential equation for mural image inpainting is mainly studied in this paper. Squared L²-norm of the fractional Laplacian is used as regularization term, the existence and uniqueness of the model are proved within the framework of fractional Sobolev spaces. Discretization of fractional Laplacian is adjusted for mural images and stability is analyzed. Experimental results show that, compared with commonly used methods, the proposed model significantly improves the PSNR and SSIM of mural inpainting, and effectively enhances the authenticity of restoring high-frequency detail information of mural images while maintaining structural consistency.

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