A Weak-Signal-Aware Framework for Subsurface Defect Detection: Mechanisms for Enhancing Low-SCR Hyperbolic Signatures

Clandestine tunneling beneath oil and gas pipelines enables fuel theft, smuggling, and sabotage, yet conventional monitoring detects damage only after a pipeline has been compromised. Ground-penetrating radar (GPR) can image such tunnels non-invasively, but manual radargram interpretation does not scale to continuous corridor surveillance, and supervised detectors require tunnel examples that are scarce in practice. We present a fully unsupervised detection pipeline trained exclusively on normal subsurface radargrams collected at a purpose-built field site containing three buried tunnels at 1.5-3 m depth. A denoising convolutional autoencoder learns the structure of anomaly-free ground; at inference, tunnels are flagged by reconstruction error. Our central contribution is a depth-restricted top-k anomaly score, which pools the highest reconstruction errors only within the depth band where tunnels can physically occur. This physically motivated rule raises AUC from 0.986 to 0.994 and cuts missed detections from 74 to 17 of 634 tunnel windows, relative to whole-image scoring, without any retraining or labels. We further show that the optimal top-k fraction interacts with the depth restriction - 1% pooling is best on full images, 5% once scoring is depth-restricted - and that spatial voting across overlapping survey windows helps weak per-image detectors but offers no benefit once the scoring rule is strong. The final system attains AUC 0.994, F1 0.975, recall 0.973, and precision 0.976 on 1,600 field test windows spanning 55 survey lines, at a 1.6% false-alarm rate, using no tunnel labels for training, scoring, or threshold calibration.

Weak spectral responses in hyperspectral images are often obscured by dominant endmembers and sensor noise, resulting in inaccurate abundance estimation. This paper introduces WS-Net, a deep unmixing framework specifically designed to address weak-signal collapse through state-space modelling and Weak Signal Attention fusion. The network features a multi-resolution wavelet-fused encoder that captures both high-frequency discontinuities and smooth spectral variations with a hybrid backbone that integrates a Mamba state-space branch for efficient long-range dependency modelling. It also incorporates a Weak Signal Attention branch that selectively enhances low-similarity spectral cues. A learnable gating mechanism adaptively fuses both representations, while the decoder leverages KL-divergence-based regularisation to enforce separability between dominant and weak endmembers. Experiments on one simulated and two real datasets (synthetic dataset, Samson, and Apex) demonstrate consistent improvements over six state-of-the-art baselines, achieving up to 55% and 63% reductions in RMSE and SAD, respectively. The framework maintains stable accuracy under low-SNR conditions, particularly for weak endmembers, establishing WS-Net as a robust and computationally efficient benchmark for weak-signal hyperspectral unmixing.

Few-shot industrial defect detection remains difficult for standard supervised detectors, which achieve poor performance on boundary-dominated industrial defects. This paper proposes rough path signature-guided geometry augmentation (RPS-GA), a geometry-aware approach in which Canny edge contours are treated as ordered planar paths whose truncated second-order signature responses, especially the antisymmetric Lévy-area term, are aggregated into a spatial map that highlights boundary-related structure through two fusion operators, SIG-AUG and SGAA. The approach is evaluated on NEU-DET and PCB-Defect under a few-shot protocol with 5, 10, 20, or 50 labeled images per class, using an unmodified YOLOv8n detector throughout. Compared with the baseline, RPS-GA delivers large gains when supervision is limited, although the margin shrinks as more labels become available. On NEU-DET, SIG-AUG raises 10-shot [email protected] from 0.341 to 0.583, whereas on PCB-Defect, SGAA improves 10-shot [email protected] from 0.086 to 0.299 and yields usable detection at 5-shot where the baseline fails entirely. These trends are confirmed by multi-seed evaluation across independent random partitions. Overall, the results indicate that second-order path-signature geometry offers a practical way to strengthen few-shot industrial defect detection without meta-learning or detector redesign.