Generative adversarial networks (GANs), trained on a large-scale image dataset, can be a good approximator of the natural image manifold. GAN-inversion, using a pre-trained generator as a deep generative prior, is a promising tool for image restoration under corruptions. However, the performance of GAN-inversion can be limited by a lack of robustness to unknown gross corruptions, i.e., the restored image might easily deviate from the ground truth. In this paper, we propose a Robust GAN-inversion (RGI) method with a provable robustness guarantee to achieve image restoration under unknown \textit{gross} corruptions, where a small fraction of pixels are completely corrupted. Under mild assumptions, we show that the restored image and the identified corrupted region mask converge asymptotically to the ground truth. Moreover, we extend RGI to Relaxed-RGI (R-RGI) for generator fine-tuning to mitigate the gap between the GAN learned manifold and the true image manifold while avoiding trivial overfitting to the corrupted input image, which further improves the image restoration and corrupted region mask identification performance. The proposed RGI/R-RGI method unifies two important applications with state-of-the-art (SOTA) performance: (i) mask-free semantic inpainting, where the corruptions are unknown missing regions, the restored background can be used to restore the missing content; (ii) unsupervised pixel-wise anomaly detection, where the corruptions are unknown anomalous regions, the retrieved mask can be used as the anomalous region's segmentation mask.

翻译：在大型图像数据集上训练的生成对抗网络（GANs）可以很好地近似自然图像流形。利用预训练生成器作为深度生成先验的GAN反演，是一种有前景的图像修复技术，可应对图像退化问题。然而，GAN反演的性能可能受限于其对未知严重退化缺乏鲁棒性，即修复图像容易偏离真实情况。本文提出一种具有可证明鲁棒性保证的稳健GAN反演（RGI）方法，能够在未知的严重退化下实现图像修复，其中少量像素被完全损坏。在温和假设下，我们证明修复后的图像和识别出的损坏区域掩码渐近收敛于真实值。此外，我们将RGI扩展为松弛版RGI（R-RGI），用于生成器微调，以缩小GAN学习流形与真实图像流形之间的差距，同时避免对损坏输入图像的过拟合，从而进一步提升图像修复和损坏区域掩码识别性能。所提出的RGI/R-RGI方法统一了两种重要应用，并取得最优性能：（i）无掩码语义修复，其中损坏是未知缺失区域，修复后的背景可用于恢复缺失内容；（ii）无监督逐像素异常检测，其中损坏是未知异常区域，检索到的掩码可作为异常区域的分割掩码。