# Biorthogonal Tunable Wavelet Unit with Lifting Scheme in Convolutional Neural Network

arXiv: https://arxiv.org/abs/2507.00739 · HTML: https://mlsanity.com/paper/2507.00739/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 18 references that are in the map.
- First posted on arXiv 1 Jul 2025.

## Builds on (most cited first, 8 of 8)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [CFLOW-AD: Real-Time Unsupervised Anomaly Detection with Localization via Conditional Normalizing Flows](https://mlsanity.com/paper/2107.12571/) (2021)
- [Spectral Representations for Convolutional Neural Networks](https://mlsanity.com/paper/1506.03767/) (2015)
- [Wavelet Integrated CNNs for Noise-Robust Image Classification](https://mlsanity.com/paper/2005.03337/) (2020)
- [Learning strides in convolutional neural networks](https://mlsanity.com/paper/2202.01653/) (2022)
- [Wavelet-Attention CNN for Image Classification](https://mlsanity.com/paper/2201.09271/) (2022)

## Built on by (most cited first, 3 of 3)

- [DWTGS: Rethinking Frequency Regularization for Sparse-view 3D Gaussian Splatting](https://mlsanity.com/paper/2507.15690/) (2025)
- [Learnable Multi-level Discrete Wavelet Transforms for 3D Gaussian Splatting Frequency Modulation](https://mlsanity.com/paper/2602.14199/) (2026)
- [Layerwise Tunable Lifting Scheme for the Convolutional Neural Network](https://mlsanity.com/paper/2609.09827/) (2026)

## Abstract (arXiv)

This work introduces a novel biorthogonal tunable wavelet unit constructed using a lifting scheme that relaxes both the orthogonality and equal filter length constraints, providing greater flexibility in filter design. The proposed unit enhances convolution, pooling, and downsampling operations, leading to improved image classification and anomaly detection in convolutional neural networks (CNN). When integrated into an 18-layer residual neural network (ResNet-18), the approach improved classification accuracy on CIFAR-10 by 2.12% and on the Describable Textures Dataset (DTD) by 9.73%, demonstrating its effectiveness in capturing fine-grained details. Similar improvements were observed in ResNet-34. For anomaly detection in the hazelnut category of the MVTec Anomaly Detection dataset, the proposed method achieved competitive and wellbalanced performance in both segmentation and detection tasks, outperforming existing approaches in terms of accuracy and robustness.