# WaveCNet: Wavelet Integrated CNNs to Suppress Aliasing Effect for Noise-Robust Image Classification

arXiv: https://arxiv.org/abs/2107.13335 · HTML: https://mlsanity.com/paper/2107.13335/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 65 references that are in the map.
- First posted on arXiv 28 Jul 2021.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [MMDetection: Open MMLab Detection Toolbox and Benchmark](https://mlsanity.com/paper/1906.07155/) (2019)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Semantic Image Segmentation with Deep Convolutional Nets and Fully Connected CRFs](https://mlsanity.com/paper/1412.7062/) (2014)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [Defense against Adversarial Attacks Using High-Level Representation Guided Denoiser](https://mlsanity.com/paper/1712.02976/) (2017)
- [Feature Denoising for Improving Adversarial Robustness](https://mlsanity.com/paper/1812.03411/) (2018)
- [High Frequency Component Helps Explain the Generalization of Convolutional Neural Networks](https://mlsanity.com/paper/1905.13545/) (2019)
- [Approximating CNNs with Bag-of-local-Features models works surprisingly well on ImageNet](https://mlsanity.com/paper/1904.00760/) (2019)
- [Why do deep convolutional networks generalize so poorly to small image transformations?](https://mlsanity.com/paper/1805.12177/) (2018)
- [Multi-level Wavelet-CNN for Image Restoration](https://mlsanity.com/paper/1805.07071/) (2018)
- [Photorealistic Style Transfer via Wavelet Transforms](https://mlsanity.com/paper/1903.09760/) (2019)
- [Wavelet Integrated CNNs for Noise-Robust Image Classification](https://mlsanity.com/paper/2005.03337/) (2020)
- [Stochastic Pooling for Regularization of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1301.3557/) (2013)
- [A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extraction](https://mlsanity.com/paper/1512.06293/) (2015)
- [WaveSNet: Wavelet Integrated Deep Networks for Image Segmentation](https://mlsanity.com/paper/2005.14461/) (2020)

## Built on by (most cited first, 29 of 29)

- [Frequency-Adaptive Dilated Convolution for Semantic Segmentation](https://mlsanity.com/paper/2403.05369/) (2024)
- [FrequencyLowCut Pooling -- Plug & Play against Catastrophic Overfitting](https://mlsanity.com/paper/2204.00491/) (2022)
- [Dynamic Sparse Training versus Dense Training: The Unexpected Winner in Image Corruption Robustness](https://mlsanity.com/paper/2410.03030/) (2024)
- [When Semantic Segmentation Meets Frequency Aliasing](https://mlsanity.com/paper/2403.09065/) (2024)
- [Activation Space Selectable Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2408.08338/) (2024)
- [Beware of Aliases -- Signal Preservation is Crucial for Robust Image Restoration](https://mlsanity.com/paper/2406.07435/) (2024)
- [From Coarse to Fine: Learnable Discrete Wavelet Transforms for Efficient 3D Gaussian Splatting](https://mlsanity.com/paper/2506.23042/) (2025)
- [DWTGS: Rethinking Frequency Regularization for Sparse-view 3D Gaussian Splatting](https://mlsanity.com/paper/2507.15690/) (2025)
- [Adversarial Attacks and Defenses in Machine Learning-Powered Networks: A Contemporary Survey](https://mlsanity.com/paper/2303.06302/) (2023)
- [BVINet: Unlocking Blind Video Inpainting with Zero Annotations](https://mlsanity.com/paper/2502.01181/) (2025)
- [Skip-WaveNet: A Wavelet based Multi-scale Architecture to Trace Snow Layers in Radar Echograms](https://mlsanity.com/paper/2310.19574/) (2023)
- [WaveDH: Wavelet Sub-bands Guided ConvNet for Efficient Image Dehazing](https://mlsanity.com/paper/2404.01604/) (2024)
- [Spatial Frequency Modulation for Semantic Segmentation](https://mlsanity.com/paper/2507.11893/) (2025)
- [Data-free Defense of Black Box Models Against Adversarial Attacks](https://mlsanity.com/paper/2211.01579/) (2022)
- [Finger-UNet: A U-Net based Multi-Task Architecture for Deep Fingerprint Enhancement](https://mlsanity.com/paper/2310.00629/) (2023)
- [The Importance of Anti-Aliasing in Tiny Object Detection](https://mlsanity.com/paper/2310.14221/) (2023)
- [Spectral U-Net: Enhancing Medical Image Segmentation via Spectral Decomposition](https://mlsanity.com/paper/2409.09216/) (2024)
- [Wavelet Integrated Convolutional Neural Network for ECG Signal Denoising](https://mlsanity.com/paper/2501.06724/) (2025)
- [WD-DETR: Wavelet Denoising-Enhanced Real-Time Object Detection Transformer for Robot Perception with Event Cameras](https://mlsanity.com/paper/2506.09098/) (2025)
- [Diffusion Models are Robust Pretrainers](https://mlsanity.com/paper/2511.02793/) (2025)
- [Learnable Multi-level Discrete Wavelet Transforms for 3D Gaussian Splatting Frequency Modulation](https://mlsanity.com/paper/2602.14199/) (2026)
- [WaveNets: Wavelet Channel Attention Networks](https://mlsanity.com/paper/2211.02695/) (2022)
- [TAOTF: A Two-stage Approximately Orthogonal Training Framework in Deep Neural Networks](https://mlsanity.com/paper/2211.13902/) (2022)
- [Fix your downsampling ASAP! Be natively more robust via Aliasing and Spectral Artifact free Pooling](https://mlsanity.com/paper/2307.09804/) (2023)
- [WCCNet: Wavelet-context Cooperative Network for Efficient Multispectral Pedestrian Detection](https://mlsanity.com/paper/2308.01042/) (2023)
- [EasyRobust: A Comprehensive and Easy-to-use Toolkit for Robust and Generalized Vision](https://mlsanity.com/paper/2503.16975/) (2025)
- [WT-BCP: Wavelet Transform based Bidirectional Copy-Paste for Semi-Supervised Medical Image Segmentation](https://mlsanity.com/paper/2504.14445/) (2025)
- [Event-to-Video Reconstruction using Spatio-Temporal and Frequency-Enhanced Deep Neural Networks](https://mlsanity.com/paper/2605.25804/) (2026)
- [Layerwise Tunable Lifting Scheme for the Convolutional Neural Network](https://mlsanity.com/paper/2609.09827/) (2026)

## Abstract (arXiv)

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 %wavelet accelerates the CNN training, and 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.