Dual High-Order Total Variation Model for Underwater Image Restoration

Underwater images are typically characterized by color cast, haze, blurring, and uneven illumination due to the selective absorption and scattering when light propagates through the water, which limits their practical applications. Underwater image enhancement and restoration (UIER) is one crucial mode to improve the visual quality of underwater images. However, most existing UIER methods concentrate on enhancing contrast and dehazing, rarely pay attention to the local illumination differences within the image caused by illumination variations, thus introducing some undesirable artifacts and unnatural color. To address this issue, an effective variational framework is proposed based on an extended underwater image formation model (UIFM). Technically, dual high-order regularizations are successfully integrated into the variational model to acquire smoothed local ambient illuminance and structure-revealed reflectance in a unified manner. In our proposed framework, the weight factors-based color compensation is combined with the color balance to compensate for the attenuated color channels and remove the color cast. In particular, the local ambient illuminance with strong robustness is acquired by performing the local patch brightest pixel estimation and an improved gamma correction. Additionally, we design an iterative optimization algorithm relying on the alternating direction method of multipliers (ADMM) to accelerate the solution of the proposed variational model. Considerable experiments on three real-world underwater image datasets demonstrate that the proposed method outperforms several state-of-the-art methods with regard to visual quality and quantitative assessments. In the quantitative assessments, the proposed method achieves average scores of 0.205 FADE, 7.688 Entropy, 0.628 UCIQE, and 0.775 FDUM across the UIEB and UIQS datasets. Moreover, the proposed method can also be extended to outdoor image dehazing and low-light image enhancement tasks. The code is available at https://github.com/HouGuojia/UDHTV.