Single-image dehazing is an important low-level vision task with many applications. Early studies have investigated different kinds of visual priors to address this problem. However, they may fail when their assumptions are not valid on specific images. Recent deep networks also achieve a relatively good performance in this task. But unfortunately, due to the disappreciation of rich physical rules in hazes, a large amount of data are required for their training. More importantly, they may still fail when there exist completely different haze distributions in testing images. By considering the collaborations of these two perspectives, this paper designs a novel residual architecture to aggregate both prior (i.e., domain knowledge) and data (i.e., haze distribution) information to propagate transmissions for scene radiance estimation. We further present a variational energy-based perspective to investigate the intrinsic propagation behavior of our aggregated deep model. In this way, we actually bridge the gap between prior-driven models and data-driven networks and leverage advantages but avoid limitations of previous dehazing approaches. A lightweight learning framework is proposed to train our propagation network. Finally, by introducing a task-aware image separation formulation with a flexible optimization scheme, we extend the proposed model for more challenging vision tasks, such as underwater image enhancement and single-image rain removal. Experiments on both synthetic and real-world images demonstrate the effectiveness and efficiency of the proposed framework.
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