This paper develops a Bayesian retinex algorithm for enhancing single underwater image with multiorder gradient priors of reflectance and illumination. First, a simple yet effective color correction approach is adopted to remove color casts and recover naturalness. Then a maximum a posteriori formulation for underwater image enhancement is established on the color-corrected image by imposing multiorder gradient priors on reflectance and illumination. The $l_1$ norm is appropriately used to model piecewise and piecewise linear approximations on the reflectance, and the $l_2$ norm is used to enforce spatial smoothness and spatial linear smoothness on the illumination. Meanwhile, a complex underwater image enhancement issue is turned into two simple denoising subproblems where their convergence analyses are mathematically provided, and their solutions can be derived by an efficient optimization algorithm. Besides, the proposed model is fast implemented on pixelwise operations while not requiring additional prior knowledge about underwater imaging conditions. Final experiments demonstrate the effectiveness of the proposed method in color correction, naturalness preservation, structures and details promotion, artifacts or noise suppression. Compared with several traditional and leading enhancement approaches, the proposed method yields better results on qualitative and quantitative assessments. The superiority of the proposed method can be extended to several challenging applications.

本文开发了一种贝叶斯retinex算法，用于利用反射和照明的多阶梯度先验来增强单个水下图像。首先，采用一种简单而有效的色彩校正方法来消除偏色并恢复自然感。然后，通过对反射率和照明施加先验多阶梯度，在色彩校正后的图像上建立用于水下图像增强的最大后验公式。这${升}_{\mathrm{1个}}$ 范数适合用于对反射率进行分段和分段线性近似建模，并且 ${升}_{\mathrm{2个}}$规范用于增强照明的空间平滑度和空间线性平滑度。同时，一个复杂的水下图像增强问题变成了两个简单的降噪子问题，在数学上提供了它们的收敛分析，并且可以通过高效的优化算法来推导它们的解决方案。此外，提出的模型可在逐像素操作上快速实现，而无需有关水下成像条件的其他先验知识。最终实验证明了该方法在色彩校正，自然保存，结构和细节提升，伪影或降噪方面的有效性。与几种传统的和领先的增强方法相比，该方法在定性和定量评估方面产生了更好的结果。