An Image Defogging Approach Based on a Constrained Energy Functional under Bayesian and Variation Theories

Hazy images produce negative influences on visual applications in the open air since they are in poor visibility with low contrast and whitening color. Numerous existing methods tend to derive a totally rough estimate of scene depth. Unlike previous work, we focus on the probability distribution of depth that is considered as a scene prior. Inspired by the denoising work of multiplicative noises, the inverse problem for hazy removal is recast as deriving the optimal difference between scene irradiance and the airlight from a constrained energy functional under Bayesian and variation theories. Logarithmic maximum a posteriori estimator and a mixed regularization term are introduced to formulate the energy functional framework where the regularization parameter is adaptively selected. The airlight, another unknown quantity, is inferred precisely under a geometric constraint and dark channel prior. With these two estimates, scene irradiance can be recovered. The experimental results on a series of hazy images reveal that, in comparison with several relevant and most state-of-the-art approaches, the proposed method outperforms in terms of vivid color and appropriate contrast.