# Wavelet-Enhanced PaDiM for Industrial Anomaly Detection

arXiv: https://arxiv.org/abs/2508.16034 · HTML: https://mlsanity.com/paper/2508.16034/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 22 Aug 2025.

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [PaDiM: a Patch Distribution Modeling Framework for Anomaly Detection and Localization](https://mlsanity.com/paper/2011.08785/) (2020)
- [Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery](https://mlsanity.com/paper/1703.05921/) (2017)
- [Memorizing Normality to Detect Anomaly: Memory-augmented Deep Autoencoder for Unsupervised Anomaly Detection](https://mlsanity.com/paper/1904.02639/) (2019)
- [GANomaly: Semi-Supervised Anomaly Detection via Adversarial Training](https://mlsanity.com/paper/1805.06725/) (2018)
- [Uninformed Students: Student-Teacher Anomaly Detection with Discriminative Latent Embeddings](https://mlsanity.com/paper/1911.02357/) (2019)
- [Sub-Image Anomaly Detection with Deep Pyramid Correspondences](https://mlsanity.com/paper/2005.02357/) (2020)
- [Improving Unsupervised Defect Segmentation by Applying Structural Similarity to Autoencoders](https://mlsanity.com/paper/1807.02011/) (2018)
- [FastFlow: Unsupervised Anomaly Detection and Localization via 2D Normalizing Flows](https://mlsanity.com/paper/2111.07677/) (2021)

## Abstract (arXiv)

Anomaly detection and localization in industrial images are essential for automated quality inspection. PaDiM, a prominent method, models the distribution of normal image features extracted by pre-trained Convolutional Neural Networks (CNNs) but reduces dimensionality through random channel selection, potentially discarding structured information. We propose Wavelet-Enhanced PaDiM (WE-PaDiM), which integrates Discrete Wavelet Transform (DWT) analysis with multi-layer CNN features in a structured manner. WE-PaDiM applies 2D DWT to feature maps from multiple backbone layers, selects specific frequency subbands (e.g., LL, LH, HL), spatially aligns them, and concatenates them channel-wise before modeling with PaDiM's multivariate Gaussian framework. This DWT-before-concatenation strategy provides a principled method for feature selection based on frequency content relevant to anomalies, leveraging multi-scale wavelet information as an alternative to random selection. We evaluate WE-PaDiM on the challenging MVTec AD dataset with multiple backbones (ResNet-18 and EfficientNet B0-B6). The method achieves strong performance in anomaly detection and localization, yielding average results of 99.32% Image-AUC and 92.10% Pixel-AUC across 15 categories with per-class optimized configurations. Our analysis shows that wavelet choices affect performance trade-offs: simpler wavelets (e.g., Haar) with detail subbands (HL or LH/HL/HH) often enhance localization, while approximation bands (LL) improve image-level detection. WE-PaDiM thus offers a competitive and interpretable alternative to random feature selection in PaDiM, achieving robust results suitable for industrial inspection with comparable efficiency.