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Hyperspectral anomaly detection using column-wise robust principal component analysis

  • role： First author第一作者
  • Affiliation：

    Department of Geography and Spatial Information Techniques, Ningbo University, Ningbo 315211, China

    State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan 430079, China

  • Email：sunweiwei@nbu.edu.cn
  • Introduction：孙伟伟(1985—　)，男，副教授，研究方向为地理信息系统、遥感理论和方法及“3S”技术在海岸带资源管理与环境变化监测中的应用。E-mail：sunweiwei@nbu.edu.cn
Weiwei SUN12,  
  • Affiliation：

    Department of Geography and Spatial Information Techniques, Ningbo University, Ningbo 315211, China

Fei LI1,  
  • Affiliation：

    Department of Geography and Spatial Information Techniques, Ningbo University, Ningbo 315211, China

Gang YANG1,  
  • Affiliation：

    Department of Geography and Spatial Information Techniques, Ningbo University, Ningbo 315211, China

Dianfa ZHANG1

resumen

Hyperspectral imagery (HSI) collects the detailed spectral response of ground objects on the Earth’s surface by using hundreds of narrow bands and presents a great potential for use in detecting anomalies (i.e., small and low-probability ground objects) from the main background. Sparsity theory has recently attracted increasing interest because of intelligent processing in the hyperspectral field. Many sparsity-based anomaly detection methods have been proposed in literature, and robust principal component analysis (RPCA)-based detectors are typical examples. However, regular RPCA-based anomaly detectors show that the sparse anomaly matrix should not be of low rank, and its nonzero entries should be randomly scattered in the matrix. This condition negatively affects the estimation of a low-rank background matrix and seriously impacts the effective separation between the background and anomalies in the image scene. Moreover, RPCA-based approaches involve many iteration procedures of primal variables, which leads to high computational complexity. Therefore, this study proposed column-wise RPCA (CWRPCA) to resolve these problems and improve the detection results. CWRPCA assumes that background information exists in low-dimensional randomized column subspace and possesses low-rank properties and that the anomalies are sparse and do not lie in the column subspace of the background. CWRPCA aims to decompose the HSI data matrix into the sum of a low-rank background matrix, a column-sparse anomaly matrix with small portions of nonzero columns, and a noise matrix. In this study, when the column subspace of the background was determined, anomalies were estimated from the nonzero columns of the anomaly matrix. The problem of determining the background and anomaly matrices was formulated into a convex optimization program in (2). The inexact augmented Lagrange multiplier algorithm was implemented to optimize the objective function. This algorithm introduces two auxiliary variables into the objective function and iteratively updates primal variables by fixing other variables. The low-rank background and sparse anomaly matrices were obtained when the iteration procedure terminated. The detection result was achieved by segmenting the L2 norms of column vectors in the anomaly matrix. Two HSI datasets were used to verify the detection performance of CWRPCA. The Receiver Operating Characteristic (ROC) curve and Area Under Curve (AUC) were utilized to evaluate detection performance. ROC describes the probabilities of detection and false alarm. AUC quantifies the area under the ROC curve and shows how far the ROC curve is from the baseline. The detection results of the proposed method were compared with those of five state-of-the-art anomaly detection methods, namely, low-rank and sparse matrix decomposition-based anomaly detection method, global Reed-Xiaoli method, dual window-based eigen separation transform, collaborative representation-based detector, and low-rank and sparse representation. Experimental results showed that the proposed CWRPCA outperformed the five state-of-the-art anomaly detection methods in temrs of ROC curve and AUC with a moderate computation cost. CWRPCA is better in detecting anomalies than other methods and can be a good alternative for hyperspectral anomaly detection.

palabra clave

hyperspectral imagery;anomaly detection;robust principal component analysis;column sparse;inexact augmented Laplacian multiplier

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