To avoid the blurred edges, noise, and halos caused by guided image filtering algorithm, this paper proposed a nonlinear gradient domain-guided image filtering algorithm for image dehazing. To dynamically adjust the edge preservation and smoothness of dehazed images, this paper proposed a fractional-order gradient descent with momentum RBF neural network to optimize the nonlinear gradient domain-guided filtering (NGDGIF-FOGDMRBF). Its convergence is proved. In order to speed up the convergence process, an adaptive learning rate is used to adjust the training process reasonably. The results verify the theoretical results of the proposed algorithm such as its monotonicity and convergence. The descending curve of error values by FOGDM is smoother than gradient descent and gradient descent with momentum method. The influence of regularization parameter is analyzed and compared. Compared with dark channel prior, histogram equalization, homomorphic filtering, and multiple exposure fusion, the halo and noise generated are significantly reduced with higher peak signal-to-noise ratio and structural similarity index.

中文翻译：

---

分数阶梯度下降和动量RBF神经网络优化的非线性梯度域引导滤波器用于舰船图像去雾

为了避免导引图像滤波算法引起的边缘模糊，噪声和光晕，提出了一种非线性梯度域导引图像滤波算法。为了动态调整去雾图像的边缘保留和平滑度，本文提出了一种带动量RBF神经网络的分数阶梯度下降算法，以优化非线性梯度域导引滤波（NGDGIF-FOGDMRBF）。证明了其收敛性。为了加快收敛过程，使用自适应学习率来合理地调整训练过程。结果验证了所提算法的单调性和收敛性等理论结果。FOGDM的误差值下降曲线比动量法的梯度下降和梯度下降更平滑。分析并比较了正则化参数的影响。与暗通道先验，直方图均衡，同态滤波和多重曝光融合相比，通过更高的峰信噪比和结构相似性指数，可以显着降低产生的光晕和噪声。