# Noise & pattern: identity-anchored Tikhonov regularization for robust structural anomaly detection

arXiv: https://arxiv.org/abs/2511.07233 · HTML: https://mlsanity.com/paper/2511.07233/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 76 references that are in the map.
- First posted on arXiv 10 Nov 2025.

## Builds on (most cited first, 30 of 35)

- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [Free-Form Image Inpainting with Gated Convolution](https://mlsanity.com/paper/1806.03589/) (2018)
- [PaDiM: a Patch Distribution Modeling Framework for Anomaly Detection and Localization](https://mlsanity.com/paper/2011.08785/) (2020)
- [Generative Image Inpainting with Contextual Attention](https://mlsanity.com/paper/1801.07892/) (2018)
- [Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery](https://mlsanity.com/paper/1703.05921/) (2017)
- [CutPaste: Self-Supervised Learning for Anomaly Detection and Localization](https://mlsanity.com/paper/2104.04015/) (2021)
- [DRAEM -- A discriminatively trained reconstruction embedding for surface anomaly detection](https://mlsanity.com/paper/2108.07610/) (2021)
- [Image Inpainting for Irregular Holes Using Partial Convolutions](https://mlsanity.com/paper/1804.07723/) (2018)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [Uninformed Students: Student-Teacher Anomaly Detection with Discriminative Latent Embeddings](https://mlsanity.com/paper/1911.02357/) (2019)
- [Deep Anomaly Detection Using Geometric Transformations](https://mlsanity.com/paper/1805.10917/) (2018)
- [Improving Unsupervised Defect Segmentation by Applying Structural Similarity to Autoencoders](https://mlsanity.com/paper/1807.02011/) (2018)
- [SimpleNet: A Simple Network for Image Anomaly Detection and Localization](https://mlsanity.com/paper/2303.15140/) (2023)
- [Gradient Magnitude Similarity Deviation: A Highly Efficient Perceptual Image Quality Index](https://mlsanity.com/paper/1308.3052/) (2013)
- [Latent Space Autoregression for Novelty Detection](https://mlsanity.com/paper/1807.01653/) (2018)
- [RealNet: A Feature Selection Network with Realistic Synthetic Anomaly for Anomaly Detection](https://mlsanity.com/paper/2403.05897/) (2024)
- [Towards Visually Explaining Variational Autoencoders](https://mlsanity.com/paper/1911.07389/) (2019)
- [Inpainting Transformer for Anomaly Detection](https://mlsanity.com/paper/2104.13897/) (2021)
- [Unsupervised Detection of Lesions in Brain MRI using constrained adversarial auto-encoders](https://mlsanity.com/paper/1806.04972/) (2018)
- [A Unified Anomaly Synthesis Strategy with Gradient Ascent for Industrial Anomaly Detection and Localization](https://mlsanity.com/paper/2407.09359/) (2024)
- [Unsupervised Anomaly Localization using Variational Auto-Encoders](https://mlsanity.com/paper/1907.02796/) (2019)
- [Towards Best Practice in Explaining Neural Network Decisions with LRP](https://mlsanity.com/paper/1910.09840/) (2019)
- [PNI : Industrial Anomaly Detection using Position and Neighborhood Information](https://mlsanity.com/paper/2211.12634/) (2022)
- [Towards Zero-Shot Anomaly Detection and Reasoning with Multimodal Large Language Models](https://mlsanity.com/paper/2502.07601/) (2025)
- [Detecting Outliers with Poisson Image Interpolation](https://mlsanity.com/paper/2107.02622/) (2021)
- [Improved anomaly detection by training an autoencoder with skip connections on images corrupted with Stain-shaped noise](https://mlsanity.com/paper/2008.12977/) (2020)
- [Do LLMs Understand Visual Anomalies? Uncovering LLM's Capabilities in Zero-shot Anomaly Detection](https://mlsanity.com/paper/2404.09654/) (2024)

## Abstract (arXiv)

Anomaly detection plays a pivotal role in automated industrial inspection, aiming to identify subtle or rare defects in otherwise uniform visual patterns. As collecting representative examples of all possible anomalies is infeasible, we tackle structural anomaly detection using a self-supervised autoencoder that learns to repair corrupted inputs. To this end, we introduce a corruption model that injects artificial disruptions into training images to mimic structural defects. While reminiscent of denoising autoencoders, our approach differs in two key aspects. First, instead of unstructured i.i.d. noise, we apply structured, spatially coherent perturbations that make the task a hybrid of segmentation and inpainting. Second, and counterintuitively, we add and preserve Gaussian noise on top of the occlusions, which acts as a Tikhonov regularizer anchoring the Jacobian of the reconstruction function toward identity. This identity-anchored regularization stabilizes reconstruction and further improves both detection and segmentation accuracy. On the MVTec AD benchmark, our method achieves state-of-the-art results (I/P-AUROC: 99.9/99.4), supporting our theoretical framework and demonstrating its practical relevance for automatic inspection.