Beer-Lambert Guided Representation Learning for Unsupervised Anomaly Detection in Sub-THz Food Inspection Images

Reconstruction-based methods are a cornerstone of unsupervised image anomaly detection, but they remain vulnerable to \emph{outlier leakage}, where standard mean squared error (MSE) loss drives the model to faithfully reconstruct anomalous patterns. We propose a Non-linear Reconstruction Loss that applies a sigmoid-based squashing function to suppress high-magnitude features, preventing outliers from dominating optimization while preserving sensitivity to normal patterns. In addition, we introduce a statistical calibration scheme that selects the scaling factor $k$ from the confidence interval (CI) of the normal feature distribution, enabling data-driven control of the suppression strength. Our approach achieves competitive or superior anomaly detection performance compared to state-of-the-art methods, reaching 99.0% Image-AUROC and 97.3% Pixel-AUROC on MVTec-AD, and 95.3% Image-AUROC and 99.0% Pixel-AUROC on VisA. These results indicate that non-linear gradient suppression is an effective mechanism for mitigating outlier leakage and improving anomaly localization in unified industrial inspection settings. The implementation is available at https://github.com/mintii13/Statistical-Non-linear-Reconstruction-Loss.git.

Reconstruction-based anomaly detection is attractive for industrial inspection, but scaling it from category-specific training to a one-for-all setting is challenging. A single model must reconstruct diverse normal appearances without copying abnormal details, which exposes two coupled failure modes: identical shortcut, where anomalies pass through the reconstruction path, and mis-reconstruction, where normal categories are confused with one another. We propose \textbf{BoRAD}, a label-free training framework that treats this as a representation-capacity allocation problem. BoRAD uses a shared learnable prototype bank to impose two complementary regularizers: spatial prototype alignment contracts local within-prototype variation to suppress anomaly copying, while prototype-relative global alignment preserves between-prototype structure and improves sensitivity to abnormal angular deviations. The prototype bank and prediction heads are used only during training; inference remains a standard teacher-student feature discrepancy pass, with no class labels, negative pairs, memory retrieval, or prototype lookup. BoRAD achieves competitive one-for-all anomaly detection performance, including 86.2% mAD on MVTec AD, 80.7% mAD on VisA and 73.1% mAD on Real-IAD. Diagnostic analyses further show reduced anomaly leakage, improved normal-category separability, and stronger anomaly-normal score separation.

Zero-shot anomaly detection (ZSAD) aims to detect anomalies and localize defective regions in unseen target domains without target training data. Recent ZSAD methods build on pretrained vision models, particularly CLIP, and construct normal and anomaly references from textual prompts or learnable visual representations. These methods perform anomaly discrimination primarily in spatial feature spaces, where subtle changes in texture, boundaries, and local structures can be confused with normal appearance variations. Although inconspicuous spatially, such defects can disrupt local texture regularity or boundary continuity, inducing response deviations across frequency bands. However, existing ZSAD methods do not explicitly model these frequency-dependent characteristics. Our image-domain analysis reveals that local defects exhibit spatial-frequency deviations from normal references across low-, middle-, and high-frequency bands, indicating that anomaly evidence is not universally dominated by high-frequency responses. Motivated by this observation, we propose FreqAnchorAD, a frequency-aware framework that organizes frequency-enhanced responses for anchor-relative anomaly discrimination. Specifically, the Local Frequency Compensation Module (LFCM) enhances intermediate patch tokens with local spatial-frequency cues. The Frequency-Deviation Anchor Projector (FDAP), our core discrimination module, organizes enhanced responses along a source-derived channel coordinate and measures anomaly evidence through relative similarity to normal and anomaly anchors. Finally, Asymmetric Anchor Supervision (AAS) stabilizes normal-anchor alignment while preserving diverse anomaly patterns. Experiments on thirteen industrial and medical benchmarks show that FreqAnchorAD achieves state-of-the-art mean performance in image-level anomaly recognition and pixel-level defect localization.