Underwater imaging faces challenges for enhancing object visibility and restoring true colors due to the absorptive and scattering characteristics of water. Underwater image restoration (UIR) seeks solutions to restore clean images from degraded ones, providing significant utility in downstream tasks. Recently, data-driven UIR has garnered much attention due to the potent expressive capabilities of deep neural networks (DNNs). These DNNs are supervised, relying on a large amount of labeled training samples. However, acquiring such data is expensive or even impossible in real-world underwater scenarios. While recent researches suggest that unsupervised learning is effective in UIR, none of these frameworks consider signal physical priors. In this work, we present a novel physics-inspired unsupervised UIR framework empowered by equivariance and unbiased estimation techniques. Specifically, equivariance stems from the invariance, inherent in natural signals to enhance data-efficient learning. Given that degraded images invariably contain noise, we propose a noise-tolerant loss for unsupervised UIR based on the Stein unbiased risk estimator to achieve an accurate estimation of the data consistency. Extensive experiments on the benchmark UIR datasets, including the UIEB and RUIE datasets, validate the superiority of the proposed method in terms of quantitative scores, visual outcomes, and generalization ability, compared to state-of-the-art counterparts. Moreover, our method demonstrates even comparable performance with the supervised model.
