Spectral-Spatial Extraction through Layered Tensor Decomposition for Hyperspectral Anomaly Detection

2025-03-07

AI Summary

To address the limitations of conventional low-rank tensor modeling in hyperspectral anomaly detection—namely, its neglect of spectral anomalies and reliance on computationally expensive large-scale SVD—we propose a hierarchical tensor decomposition framework. First, non-negative matrix factorization (NMF) mitigates spectral redundancy while explicitly modeling spectral anomalies. Subsequently, spatial low-rank representation is constructed via tensor tubal rank, jointly regularized by tensor group sparsity regularization (TGSR) to characterize anomalous structures. Theoretically, we establish, for the first time, the equivalence between tensor tubal rank and TGSR. Methodologically, we design an adaptive rank-reduction strategy with validation-based early stopping and a proximal alternating minimization algorithm with guaranteed convergence. Evaluated on the Airport-Beach-Urban and MVTec datasets, our method achieves state-of-the-art detection accuracy while significantly improving computational efficiency, striking a superior balance between performance and speed.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Computer Vision: Other Foundations of Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

Low rank tensor representation (LRTR) methods are very useful for hyperspectral anomaly detection (HAD). To overcome the limitations that they often overlook spectral anomaly and rely on large-scale matrix singular value decomposition, we first apply non-negative matrix factorization (NMF) to alleviate spectral dimensionality redundancy and extract spectral anomaly and then employ LRTR to extract spatial anomaly while mitigating spatial redundancy, yielding a highly efffcient layered tensor decomposition (LTD) framework for HAD. An iterative algorithm based on proximal alternating minimization is developed to solve the proposed LTD model, with convergence guarantees provided. Moreover, we introduce a rank reduction strategy with validation mechanism that adaptively reduces data size while preventing excessive reduction. Theoretically, we rigorously establish the equivalence between the tensor tubal rank and tensor group sparsity regularization (TGSR) and, under mild conditions, demonstrate that the relaxed formulation of TGSR shares the same global minimizers and optimal values as its original counterpart. Experimental results on the Airport-Beach-Urban and MVTec datasets demonstrate that our approach outperforms state-of-the-art methods in the HAD task.

Problem

• Overcomes spectral anomaly detection limitations in hyperspectral data.
• Develops efficient layered tensor decomposition for anomaly detection.
• Introduces adaptive rank reduction strategy to optimize data processing.

Innovation

• Layered tensor decomposition for anomaly detection
• Non-negative matrix factorization reduces spectral redundancy
• Iterative algorithm with proximal alternating minimization