A Method for Restoring Dunhuang Murals Based on Improved Generative Adversarial Networks

Due to long-term natural weathering and environmental erosion, the murals of the Dunhuang Mogao Caves commonly suffer from degradation issues such as fading, flaking, cracking, and large-scale structural damage. Existing deep learning-based image inpainting methods frequently suffer from structural discontinuities, pattern distortion, and local semantic inconsistencies when processing images with complex line drawings and distinctive cultural patterns, such as Dunhuang murals. To address these challenges, this paper proposes HT-GAN, a Dunhuang mural restoration framework that integrates Hankel-Tucker low-rank structural modeling with generative adversarial learning. This framework enhances structural continuity and pattern consistency within complex damaged regions through explicit low-rank structural constraints. Specifically, the proposed method models local mural features as Hankel tensors and utilizes Tucker decomposition to extract low-rank structural correlations. These correlations are then embedded into the feature learning process of the generator, enabling the joint optimization of structural priors and texture generation. Furthermore, a two-stage progressive generation mechanism consisting of "coarse-to-fine" restoration is developed. The coarse restoration stage aims to reconstruct the overall contours and low-frequency semantic structures of the damaged regions, while the fine restoration stage incorporates dilated convolutions, skip connections, and PatchGAN adversarial constraints to further enhance local texture details and edge realism. Experiments were conducted on a Dunhuang mural dataset, and a comprehensive evaluation was performed using objective metrics including PSNR, SSIM, and MSE. Quantitative results indicate that the proposed method achieves a PSNR of 41.13 dB, an SSIM of 0.9779, and a low MSE of 0.000440 on the validation set, significantly outperforming several state-of-the-art image inpainting methods in terms of structural continuity, pattern consistency, and visual naturalness. Ablation studies further validate the indispensability of both the Hankel-Tucker module and the two-stage generation mechanism. This work provides a novel approach that balances structural controllability and visual realism for the non-destructive digital restoration of cultural heritage images, such as the Dunhuang murals.