Depth-map-awared underwater image restoration using variational guided regularization

Underwater images often suffer from degradation due to the absorption and scattering of light, resulting in low visibility and turbid visual effects. To address this problem, we propose a depth-map-awared variational regularization model for underwater image restoration. First, we utilize deep learning techniques to preliminarily estimate a depth map based on the underwater image light attenuation prior. Next, we establish a variational regularization model that simultaneously refines the estimated depth map and restores the underwater images. The proposed model incorporates a total variation regularization term for the restored image and a guided regularization term for the depth map. This guided regularization term constrains the depth map to approximate the initially estimated depth while also enforcing fractional-order ($s\in (0,1)$) smoothness. Furthermore, we demonstrate the convexity of the model, ensuring the existence and uniqueness of solutions. Finally, we employ the alternating direction method of multipliers (ADMM) to solve the proposed model. Extensive experiments show that our model outperforms several state-of-the-art restoration techniques, with significant improvements in image quality as measured by the no-reference underwater color image quality evaluation (UCIQE) and fog-aware density evaluator (FADE).