# High Dimensional Data Decomposition for Anomaly Detection of Textured Images

arXiv: https://arxiv.org/abs/2512.20432 · HTML: https://mlsanity.com/paper/2512.20432/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 39 references that are in the map.
- First posted on arXiv 23 Dec 2025.

## Builds on (most cited first, 4 of 4)

- [Anomaly Detection via Self-organizing Map](https://mlsanity.com/paper/2107.09903/) (2021)
- [Distance-Based Anomaly Detection for Industrial Surfaces Using Triplet Networks](https://mlsanity.com/paper/2011.04121/) (2020)
- [A Robust Asymmetric Kernel Function for Bayesian Optimization, with Application to Image Defect Detection in Manufacturing Systems](https://mlsanity.com/paper/2109.10898/) (2021)
- [Tensor decomposition to Compress Convolutional Layers in Deep Learning](https://mlsanity.com/paper/2005.13746/) (2020)

## Abstract (arXiv)

In the realm of diverse high-dimensional data, images play a significant role across various processes of manufacturing systems where efficient image anomaly detection has emerged as a core technology of utmost importance. However, when applied to textured defect images, conventional anomaly detection methods have limitations including non-negligible misidentification, low robustness, and excessive reliance on large-scale and structured datasets. This paper proposes a texture basis integrated smooth decomposition (TBSD) approach, which is targeted at efficient anomaly detection in textured images with smooth backgrounds and sparse anomalies. Mathematical formulation of quasi-periodicity and its theoretical properties are investigated for image texture estimation. TBSD method consists of two principal processes: the first process learns the texture basis functions to effectively extract quasi-periodic texture patterns; the subsequent anomaly detection process utilizes that texture basis as prior knowledge to prevent texture misidentification and capture potential anomalies with high accuracy.The proposed method surpasses benchmarks with less misidentification, smaller training dataset requirement, and superior anomaly detection performance on both simulation and real-world datasets.