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Demeaned Sparse: Efficient Anomaly Detection by Residual Estimate
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Proposes a demeaned Fourier-domain factor-model test for image anomalies and a DFS module that learns Fourier masks to sparsify images before a U-Net reconstruction for unsupervised anomaly detection on MVTec-AD and VisA.
Problem
Unsupervised image anomaly detection with reconstruction-based methods lacks an interpretable theoretical framework guaranteeing detection effectiveness; frequency-domain methods work empirically but without theory.
Approach
Adapts a DFT-based structural-change test for factor models (Fu et al., 2023) to 2D images by applying a demeaned multi-dimensional Fourier transform to residuals, and uses it to derive a learnable Bernoulli-style Fourier mask (DFS) that sparsifies the input before reconstruction, with the mask optimized in a bootstrap-like manner.
Key results
- On MVTec-AD, Ours achieves average Img-AUROC 98.69, Pix-AUROC 98.32, PRO 93.24, versus Ours-Base 95.04 / 96.59 / 84.10 (improvements of 3.65, 1.73, 9.14 points).
- On VisA, Ours achieves average Img-AUROC 96.34, Pix-AUROC 98.19, PRO 91.15, versus Ours-Base 94.88 / 97.63 / 86.13.
- Ours uses 28.37M params and 38.20 GFLOPs, fewer than most reconstruction baselines in Table 4 (e.g., DRAEM 97.42M, 198.66G).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the DFS module to the reconstruction network (ablation) | DFS-AD · MVTec-AD average | Img-AUROC: 95.04 -> 98.69 | Helped |
| Add the DFS module to the reconstruction network (ablation) | DFS-AD · MVTec-AD average | Pix-AUROC: 96.59 -> 98.32 | Helped |
| Add the DFS module to the reconstruction network (ablation) | DFS-AD · MVTec-AD average | PRO: 84.10 -> 93.24 | Helped |
| Add the DFS module to the reconstruction network (ablation) | DFS-AD · VisA average | Img-AUROC: 94.88 -> 96.34 | Helped |
| Add the DFS module to the reconstruction network (ablation) | DFS-AD · VisA average | Pix-AUROC: 97.63 -> 98.19 | Helped |
| Add the DFS module to the reconstruction network (ablation) | DFS-AD · VisA average | PRO: 86.13 -> 91.15 | Helped |
Surprising findings
- Ours has lower average Img-AUROC on MVTec-AD than TransFusion (99.42) and PatchCore (98.96), so it is not uniformly best.
- Performance of Ours degrades sharply at higher resolutions on MVTec-AD (Img-AUROC 85.11 for Ours-Base at 512 vs 98.69 for Ours at 256 is not comparable; Ours at 1024 averages 97.19 Img-AUROC but Pix-AUROC drops to 91.49).
Limitations
- Theoretical results rely on many assumptions (factor moments, weak dependence, martingale difference residuals) and are only sketched in the main text.
- Statistical significance testing is acknowledged as necessary but not reported; metrics are AUROC/PRO only.
- Average Img-AUROC on MVTec-AD is below TransFusion and PatchCore, and performance varies across resolutions.
Experimental setup
Datasets: MVTec-AD VisA
Benchmarks: MVTec-AD VisA
Metrics: Img-AUROC Pix-AUROC PRO
Baselines: PatchCore PyramidFlow SSNF DRAEM IFgNet TransFusion Ours-Base
Builds on: Fu et al. (2023) DFT-based structural change test DRAEM U-Net
Closest papers by meaning
- Correcting Deviations from Normality: A Reformulated Diffusion Model for Multi-Class Unsupervised Anomaly Detection (CVPR 2025 · similarity 0.86)
- A Diffusion-Based Framework for Multi-Class Anomaly Detection (AAAI 2024 · similarity 0.85)
- Dual-Interrelated Diffusion Model for Few-Shot Anomaly Image Generation (CVPR 2025 · similarity 0.85)
- DZAD: Diffusion-based Zero-shot Anomaly Detection (AAAI 2025 · similarity 0.84)
- AnomalyDiffusion: Few-Shot Anomaly Image Generation with Diffusion Model (AAAI 2024 · similarity 0.83)
- Generating and Reweighting Dense Contrastive Patterns for Unsupervised Anomaly Detection (AAAI 2024 · similarity 0.83)
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