Though widely used in image classification, convolutional neural networks (CNNs) are prone to noise interruptions, i.e. the CNN output can be drastically changed by small image noise. To improve the noise robustness, we try to integrate CNNs with wavelet by replacing the common down-sampling (max-pooling, strided-convolution, and average pooling) with discrete wavelet transform (DWT). We firstly propose general DWT and inverse DWT (IDWT) layers applicable to various orthogonal and biorthogonal discrete wavelets like Haar, Daubechies, and Cohen, etc., and then design wavelet integrated CNNs (WaveCNets) by integrating DWT into the commonly used CNNs (VGG, ResNets, and DenseNet). During the down-sampling, WaveCNets apply DWT to decompose the feature maps into the low-frequency and high-frequency components. Containing the main information including the basic object structures, the low-frequency component is transmitted into the following layers to generate robust high-level features. The high-frequency components are dropped to remove most of the data noises. The experimental results show that WaveCNets achieve higher accuracy on ImageNet than various vanilla CNNs. We have also tested the performance of WaveCNets on the noisy version of ImageNet, ImageNet-C and six adversarial attacks, the results suggest that the proposed DWT/IDWT layers could provide better noise-robustness and adversarial robustness. When applying WaveCNets as backbones, the performance of object detectors (i.e., faster R-CNN and RetinaNet) on COCO detection dataset are consistently improved. We believe that suppression of aliasing effect, i.e. separation of low frequency and high frequency information, is the main advantages of our approach. The code of our DWT/IDWT layer and different WaveCNets are available at https://github.com/CVI-SZU/WaveCNet .

中文翻译：

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WaveCNet：小波集成 CNN 抑制混叠效应，实现抗噪图像分类


尽管卷积神经网络 (CNN) 广泛应用于图像分类，但它很容易受到噪声干扰，即 CNN 的输出可能会因微小的图像噪声而发生巨大变化。为了提高噪声鲁棒性，我们尝试将 CNN 与小波集成，用离散小波变换 (DWT) 代替常见的下采样（最大池化、跨步卷积和平均池化）。我们首先提出适用于 Haar、Daubechies 和 Cohen 等各种正交和双正交离散小波的通用 DWT 和逆 DWT (IDWT) 层，然后通过将 DWT 集成到常用的 CNN (VGG) 中来设计小波集成​​ CNN (WaveCNets) 、ResNet 和 DenseNet）。在下采样过程中，WaveCNet 应用 DWT 将特征图分解为低频和高频分量。低频分量包含基本对象结构等主要信息，被传输到后续层以生成鲁棒的高级特征。高频成分被丢弃以消除大部分数据噪声。实验结果表明，WaveCNet 在 ImageNet 上比各种普通 CNN 实现了更高的准确率。我们还在 ImageNet、ImageNet-C 的噪声版本和六种对抗性攻击上测试了 WaveCNets 的性能，结果表明所提出的 DWT/IDWT 层可以提供更好的噪声鲁棒性和对抗鲁棒性。当应用 WaveCNet 作为主干时，COCO 检测数据集上的对象检测器（即更快的 R-CNN 和 RetinaNet）的性能得到持续改进。我们相信，抑制混叠效应，即低频和高频信息的分离，是我们方法的主要优点。 我们的 DWT/IDWT 层和不同 WaveCNet 的代码可在 https://github.com/CVI-SZU/WaveCNet 上找到。