Adams-based hierarchical features fusion network for image dehazing.

Recent developments in Convolutional Neural Networks (CNNs) have made them one of the most powerful image dehazing methods. In particular, the Residual Networks (ResNets), which can avoid the vanishing gradient problem effectively, are widely deployed. To understand the success of ResNets, recent mathematical analysis of ResNets reveals that a ResNet has a similar formulation as the Euler method in solving the Ordinary Differential Equations (ODE's). Hence, image dehazing which can be formulated as an optimal control problem in dynamical systems can be solved by a single-step optimal control method, such as the Euler method. This optimal control viewpoint provides a new perspective to address the problem of image restoration. Motivated by the advantages of multi-step optimal control solvers in ODE's, which include better stability and efficiency than single-step solvers, e.g. Euler, we propose the Adams-based Hierarchical Feature Fusion Network (AHFFN) for image dehazing with modules inspired by a multi-step optimal control method named the Adams-Bashforth method. Firstly, we extend a multi-step Adams-Bashforth method to the corresponding Adams block, which achieves a higher accuracy than that of single-step solvers because of its more effective use of intermediate results. Then, we stack multiple Adams blocks to mimic the discrete approximation process of an optimal control in a dynamical system. To improve the results, the hierarchical features from stacked Adams blocks are fully used by combining Hierarchical Feature Fusion (HFF) and Lightweight Spatial Attention (LSA) with Adams blocks to form a new Adams module. Finally, we not only use HFF and LSA to fuse features, but also highlight important spatial information in each Adams module for estimating the clear image. The experimental results using synthetic and real images demonstrate that the proposed AHFFN obtains better accuracy and visual results than that of state-of-the-art methods.