Wavelet-Enhanced PaDiM for Industrial Anomaly Detection

Anomaly detection (AD) and localization in industrial images are essential for automated quality inspection. PaDiM models normality using multivariate Gaussian distributions over deep features, but typically relies on random channel selection for dimensionality reduction. This limits interpretability and potentially discards structured information. We propose Wavelet-Enhanced PaDiM (WE-PaDiM), which replaces random selection with a structured frequency-domain feature selection strategy using the 2D Discrete Wavelet Transform (DWT) as its core component to decompose CNN features into interpretable frequency subbands before modeling. Specifically, DWT is applied independently to multi-layer CNN feature maps, selected subband coefficients are spatially aligned, and the resulting representations are concatenated prior to PaDiM modeling. We evaluate WE-PaDiM on MVTec AD and VisA datasets across ResNet-18 and EfficientNet-b0–b6 backbones. Under per-category configuration selection, WE-PaDiM achieves 99.32% Image-AUC on MVTec AD (image-optimized) and 96.65% Pixel-AUC (pixel-optimized), and achieves 93.59% Image-AUC on VisA (image-optimized) and 96.43% Pixel-AUC (pixel-optimized). These image- and pixel-optimized results correspond to distinct operating points (potentially selecting different configurations), rather than a single jointly-achieved setting. Notably, the dominant fixed pixel-level operating point is Haar/L1/LL (low-frequency) on both datasets, while per-category pixel-optimal selections are largely LL-dominant with a small number of VisA exceptions. WE-PaDiM offers deterministic and interpretable feature selection with competitive computational characteristics.