  Convolutional Neural Networks (CNNs) are generally prone to noise
interruptions, i.e., small image noise can cause drastic changes in the output.
To suppress the noise effect to the final predication, we enhance CNNs by
replacing max-pooling, strided-convolution, and average-pooling with Discrete
Wavelet Transform (DWT). We present general DWT and Inverse DWT (IDWT) layers
applicable to various wavelets like Haar, Daubechies, and Cohen, etc., and
design wavelet integrated CNNs (WaveCNets) using these layers for image
classification. In WaveCNets, feature maps are decomposed into the
low-frequency and high-frequency components during the down-sampling. The
low-frequency component stores main information including the basic object
structures, which is transmitted into the subsequent layers to extract robust
high-level features. The high-frequency components, containing most of the data
noise, are dropped during inference to improve the noise-robustness of the
WaveCNets. Our experimental results on ImageNet and ImageNet-C (the noisy
version of ImageNet) show that WaveCNets, the wavelet integrated versions of
VGG, ResNets, and DenseNet, achieve higher accuracy and better noise-robustness
than their vanilla versions.
