Low-Rank Representations Meets Deep Unfolding: A Generalized and Interpretable Network for Hyperspectral Anomaly Detection

TL;DR

This work tackles hyperspectral anomaly detection (HAD) under limited data and interpretable requirements by introducing AIR-HAD, a challenging large-scale benchmark, and proposing LRR-Net$^+$, a deep-unfolded HAD network that melds a dictionary-learnable low-rank representation (LRR) model with ADMM-based optimization. The network unrolls the ADMM steps into five sub-networks, enabling simultaneous updates of dictionary atoms and coefficients and learning regularization parameters, while maintaining interpretability through a physics-informed prior. Empirical results on AIR-HAD and ABU datasets show that LRR-Net$^+$ consistently outperforms traditional HAD methods and prior deep-learning approaches in detection performance and robustness to background interference, with the optimization converging effectively within about 40 stages. The work contributes a large-scale HAD benchmark, a principled interpretable network that integrates model-based priors with deep learning, and open-source resources to advance HAD research and applications.

Abstract

Current hyperspectral anomaly detection (HAD) benchmark datasets suffer from low resolution, simple background, and small size of the detection data. These factors also limit the performance of the well-known low-rank representation (LRR) models in terms of robustness on the separation of background and target features and the reliance on manual parameter selection. To this end, we build a new set of HAD benchmark datasets for improving the robustness of the HAD algorithm in complex scenarios, AIR-HAD for short. Accordingly, we propose a generalized and interpretable HAD network by deeply unfolding a dictionary-learnable LLR model, named LRR-Net$^+$, which is capable of spectrally decoupling the background structure and object properties in a more generalized fashion and eliminating the bias introduced by vital interference targets concurrently. In addition, LRR-Net$^+$ integrates the solution process of the Alternating Direction Method of Multipliers (ADMM) optimizer with the deep network, guiding its search process and imparting a level of interpretability to parameter optimization. Additionally, the integration of physical models with DL techniques eliminates the need for manual parameter tuning. The manually tuned parameters are seamlessly transformed into trainable parameters for deep neural networks, facilitating a more efficient and automated optimization process. Extensive experiments conducted on the AIR-HAD dataset show the superiority of our LRR-Net$^+$ in terms of detection performance and generalization ability, compared to top-performing rivals. Furthermore, the compilable codes and our AIR-HAD benchmark datasets in this paper will be made available freely and openly at \url{https://sites.google.com/view/danfeng-hong}.

Figures (10)

• Figure 1: Pseudo-color images of different public data sets in hyperspectral anomaly detection.
• Figure 2: Visualization of AIR-HAD data set, and anomalous targets are shown marked by yellow boxes. (a)-(c) denote the data sets AIR-HAD-Resident, AIR-HAD-Vehicle-I, and AIR-HAD-Vehicle-II, respectively.
• Figure 3: An illustration of the iterative learning process of the deep unfolding LRR model in the proposed LRR-Net$^+$ network. The to-be-estimated variables $\mathbf{D}$, $\mathbf{L}$, $\mathbf{S}$, $\mathbf{J}$, and $\mathbf{d}$ denote the dictionary atoms, dictionary coefficients, anomaly vectors, auxiliary variables, and Lagrangian multipliers, respectively.
• Figure 4: Image descriptions and detection maps of Airport 1 to 4, showing (a) false-color images, (b) corresponding ground truth, and the detection maps corresponding to (c)–(j) Global-RX, Local-RX, CRD, LRASR, CNN, Auto-AD, LRR-Net, and LRR-Net$^+$ respectively.
• Figure 5: Image descriptions and detection maps of AIR-HAD-Vehicle-II, showing (a) false-color images, (b) corresponding ground truth, and the detection maps corresponding to (c)–(j) Global-RX, Local-RX, CRD, LRASR, CNN, Auto-AD, LRR-Net, and LRR-Net$^+$ respectively.