Bayesian retinex underwater image enhancement

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 l1 norm is appropriately used to model piecewise and piecewise linear approximations on the reflectance, and the l2 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.