  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.
