Single image rain streak removal is a well-explored topic in the field of computer vision. The de-raining problem is modeled as an image decomposition task where a rainy image is decomposed into rain-free background image and rain streek map. Unlike most of the existing de-raining methods, this paper attempts to decompose the rainy image in the frequency domain. The idea is inspired by pseudo-periodic characteristics of the noise signal (here the rain streaks) which leave some traces in the frequency domain, and the same can be utilized to predict the noise signal. In this paper, a deep learning-based rain streak prediction model is proposed which learns in discrete Fourier transform Oppenheim and Schafer (Discrete-TimeSignal Processing, Prentice Hall, Upper Saddle River, 1989) domain. To the best of our knowledge, this is the first approach where compressed domain coefficients are directly used as input to a deep convolutional neural network. The proposed model has been tested on publicly available synthetic datasets Fu et al. (in: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017. https://doi.org/10.1109/CVPR.2017.186 , Yang et al. (in: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017. https://doi.org/10.1109/CVPR.2017.183 ), Yeh et al. (in: 2015 IEEE International Conference on Consumer Electronics-Taiwan, 2015. https://doi.org/10.1109/ICCE-TW.2015.7216999 ) and results are found to be comparable with the state of the art methods in the spatial domain. The presented analysis and study have an obvious indication to extend transform domain input to train the deep learning architecture especially image de-noising like problems.

中文翻译：

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使用离散傅立叶变换的基于深度学习的图像去雨

单幅图像雨痕去除是计算机视觉领域中一个深入探讨的话题。去雨问题被建模为图像分解任务，其中雨图像被分解为无雨背景图像和雨条纹图。与现有的大多数去雨方法不同，本文尝试在频域分解雨图像。这个想法的灵感来自噪声信号（这里是雨条纹）的伪周期特性，它在频域中留下一些痕迹，同样可以用来预测噪声信号。在本文中，提出了一种基于深度学习的连续降雨预测模型，该模型在离散傅立叶变换 Oppenheim 和 Schafer（离散时间信号处理，Prentice Hall，Upper Saddle River，1989）域中学习。据我们所知，这是第一种将压缩域系数直接用作深度卷积神经网络输入的方法。所提出的模型已在公开可用的合成数据集 Fu 等人上进行了测试。(in: 2017 IEEE Con​​ference on Computer Vision and Pattern Recognition (CVPR), 2017. https://doi.org/10.1109/CVPR.2017.186 , Yang et al. (in: 2017 IEEE Con​​ference on Computer Vision and Pattern Recognition (CVPR) ), 2017. https://doi.org/10.1109/CVPR.2017.183 ), Yeh et al. (in: 2015 IEEE International Conference on Consumer Electronics-Taiwan, 2015. https://doi.org/10.1109/ICCE- TW.2015.7216999 ) 并且发现结果与空间域中的最先进方法相当。