Department of Computing and Artificial Intelligence, Southwestern University of Finance and Economics, Chengdu, Sichuan, 611130, China; Kash Institute of Electronics and Information Industry, Xinjiang, 844000, China; Complex Laboratory of New Finance and Economics, Southwestern University of Finance and Economics, Chengdu, Sichuan, 611130, China.
Department of Computing and Artificial Intelligence, Southwestern University of Finance and Economics, Chengdu, Sichuan, 611130, China.
Neural Netw. 2023 Jun;163:379-394. doi: 10.1016/j.neunet.2023.03.021. Epub 2023 Mar 21.
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.
卷积神经网络（CNN）的最新发展使其成为最强大的图像去雾方法之一。特别是可以有效避免梯度消失问题的残差网络（ResNets）得到了广泛应用。为了理解 ResNets 的成功，最近对 ResNets 的数学分析表明，ResNet 的公式与求解常微分方程（ODE）的 Euler 方法相似。因此，图像去雾可以被表述为动力系统中的最优控制问题，可以通过单步最优控制方法（例如 Euler 方法）来解决。这种最优控制观点为解决图像恢复问题提供了新的视角。受多步最优控制求解器在 ODE 中的优势的启发，包括比单步求解器（例如 Euler 方法）更好的稳定性和效率，我们提出了基于 Adams 的分层特征融合网络（AHFFN）用于图像去雾，该网络的模块受到一种名为 Adams-Bashforth 方法的多步最优控制方法的启发。首先，我们将多步 Adams-Bashforth 方法扩展到相应的 Adams 块，由于更有效地利用中间结果，它比单步求解器具有更高的精度。然后，我们堆叠多个 Adams 块以模拟动力系统中最优控制的离散逼近过程。为了提高结果，通过将分层特征融合（HFF）和轻量化空间注意力（LSA）与 Adams 块结合使用，充分利用堆叠 Adams 块的分层特征，形成新的 Adams 模块。最后，我们不仅使用 HFF 和 LSA 进行特征融合，而且还突出了每个 Adams 模块中的重要空间信息，以用于估计清晰图像。使用合成和真实图像进行的实验结果表明，与最先进的方法相比，所提出的 AHFFN 具有更好的准确性和视觉效果。
