列式鲁棒主成分分析的高光谱遥感异常探测
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摘要
传统的基于鲁棒主成分分析的高光谱异常探测模型中,稀疏异常矩阵假设为非低秩且其非零元素满足随机分布条件。这导致稀疏矩阵的非零元素影响低秩背景矩阵的估计,进而制约背景信息和异常信息的有效分离。提出列式鲁棒主成分分析的异常探测方法,改进异常矩阵为列稀疏条件来解决上述问题。该方法分解高光谱影像2维矩阵为低秩背景矩阵,列稀疏异常矩阵和噪声矩阵,松弛目标方程为凸优化问题,并采用非精确增强拉格朗日乘子算法来求解得到列稀疏异常矩阵的最优估计。最后,对稀疏异常矩阵中所有列的L2范数值进行阈值分割来探测得到异常像元。利用两个高光谱影像数据集,对比5种主流的异常探测方法来验证提出方法的有效性。实验结果表明,列式鲁棒主成分分析方法优于包括传统鲁棒主成分分析模型在内的5种异常探测方法,且计算效率适中。
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, RPCAbased 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 decompositionbased anomaly detection method, global Reed-Xiaoli method, dual window-based eigen separation transform, collaborative representationbased 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.
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, RPCAbased 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 decompositionbased anomaly detection method, global Reed-Xiaoli method, dual window-based eigen separation transform, collaborative representationbased 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.
引文
Candes E J,Li X D,Ma Y and Wright J.2009.Robust principal component analysis?ar Xiv:0912.3599
Chen Y D,Xu H,Caramanis C and Sanghavi S.2011.Robust matrix completion and corrupted columns//Proceedings of the 28th International Conference on Machine Learning.Bellevue,WA,USA:ICML:873-880.
Cui X Q,Tian Y,Weng L B and Yang Y P.2014.Anomaly detection in hyperspectral imagery based on low-rank and sparse decomposition//Proceedings of SPIE Volume 9069,Fifth International Conference on Graphic and Image Processing.Hong Kong,China:SPIE:90690R[DOI:10.1117/12.2050229]
Du P J,Xia J S,Xue C H,Tan K,Su H J and Bao R.2016.Review of hyperspectral remote sensing image classification.Journal of Remote Sensing,20(2):236-256(杜培军,夏俊士,薛朝辉,谭琨,苏红军,鲍蕊.2016.高光谱遥感影像分类研究进展.遥感学报,20(2):236-256)[DOI:10.11834/jrs.20165022]
Kwon H,Der S Z and Nasrabadi N M.2003.Adaptive anomaly detection using subspace separation for hyperspectral imagery.Optical Engineering,42(11):3342-3351[DOI:10.1117/1.1614265]
Li W and Du Q.2015.Collaborative representation for hyperspectral anomaly detection.IEEE Transactions on Geoscience and Remote Sensing,53(3):1463-1474[DOI:10.1109/TGRS.2014.2343955]
Lin Z,Ganesh A,Wright J,Wu L,Chen M and Ma Y.2009.Fast convex optimization algorithms for exact recovery of a corrupted lowrank matrix.Proceedings in International workshops on Computational Advances in Multi-Sensor Adaptive Processing(CAMSAP),1-18[DOI:10.1.1.231.4169]
Lin Z C,Chen M M and Ma Y.2010.The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices.ar Xiv:1009.5055
Liu G C,Lin Z C,Yan S C,Sun J,Yu Y and Ma Y.2013.Robust recovery of subspace structures by low-rank representation.IEEETransactions on Pattern Analysis and Machine Intelligence,35(1):171-184[DOI:10.1109/TPAMI.2012.88]
Liu W M and Chang C I.2013.Multiple-window anomaly detection for hyperspectral imagery.IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing,6(2):644-658plied Earth Observations and Remote Sensing,6(2):644-658[DOI:10.1109/JSTARS.2013.2239959]
Nasrabadi N M.2014.Hyperspectral target detection:an overview of current and future challenges.IEEE Signal Processing Magazine,31(1):34-44[DOI:10.1109/MSP.2013.2278992]
Rahmani M and Atia G.2015.Randomized robust subspace recovery for high dimensional data matrices.ar Xiv:1505.05901
Reed I S and Yu X.1990.Adaptive multiple-band CFAR detection of an optical pattern with unknown spectral distribution.IEEE Transactions on Acoustics,Speech,and Signal Processing,38(10):1760-1770[DOI:10.1109/29.60107]
Sun W W,Liu C,Li J L,Lai Y M and Li W Y.2014.Low-rank and sparse matrix decomposition-based anomaly detection for hyperspectral imagery.Journal of Applied Remote Sensing,8(1):083641[DOI:10.1117/1.JRS.8.083641]
Sun W W,Yang G,Du B,Zhang L F and Zhang L P.2017.A sparse and low-rank near-isometric linear embedding method for feature extraction in hyperspectral imagery classification.IEEE Transactions on Geoscience and Remote Sensing,55(7):4032-4046[DOI:10.1109/TGRS.2017.2686842]
Tong Q X,Zhang B and Zhang L F.2016.Current progress of hyperspectral remote sensing in China.Journal of Remote Sensing,20(5):689-707(童庆禧,张兵,张立福.2016.中国高光谱遥感的前沿进展.遥感学报,20(5):689-707)[DOI:10.11834/jrs.20166264]
Wang Y M,Jia J X,He Z P and Wang J Y.2016.Key technologies of advanced hyperspectral imaging system.Journal of Remote Sensing,20(5):850-857(王跃明,贾建鑫,何志平,王建宇.2016.若干高光谱成像新技术及其应用研究.遥感学报,20(5):850-857)[DOI:10.11834/jrs.20166206]
Wu Z B,Li Y L,Plaza A,Li J,Xiao F and Wei Z H.2016.Parallel and distributed dimensionality reduction of hyperspectral data on cloud computing architectures.IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing,9(6):2270-2278[DOI:10.1109/JSTARS.2016.2542193]
Xu H,Caramanis C and Sanghavi S.2010.Robust PCA via outlier pursuit//Proceedings of the 23rd International Conference on Neural Information Processing Systems.Vancouver,British Columbia,Canada:Curran Associates Inc.:2496-2504
Xu Y,Wu Z B,Li J,Plaza A and Wei Z H.2016.Anomaly detection in hyperspectral images based on low-rank and sparse representation.IEEE Transactions on Geoscience and Remote Sensing,54(4):1990-2000[DOI:10.1109/TGRS.2015.2493201]
Zhang L P,Du B and Zhong Y F.2010.Hybrid detectors based on selective endmembers.IEEE Transactions on Geoscience and Remote Sensing,48(6):2633-2646[DOI:10.1109/TGRS.2010.2040284]
Zhang L P and Li J Y.2016.Development and prospect of sparse representation-based hyperspectral image processing and analysis.Journal of Remote Sensing,20(5):1091-1101(张良培,李家艺.2016.高光谱图像稀疏信息处理综述与展望.遥感学报,20(5):1091-1101)[DOI:10.11834/jrs.20166050]
Zhang Y X,Du B and Zhang L P.2015.A sparse representation-based binary hypothesis model for target detection in hyperspectral images.IEEE Transactions on Geoscience and Remote Sensing,53(3):1346-1354[DOI:10.1109/TGRS.2014.2337883]
Zhao R,Du B and Zhang L P.2014.A robust nonlinear hyperspectral anomaly detection approach.IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing,7(4):1227-1234[DOI:10.1109/JSTARS.2014.2311995]
Chen Y D,Xu H,Caramanis C and Sanghavi S.2011.Robust matrix completion and corrupted columns//Proceedings of the 28th International Conference on Machine Learning.Bellevue,WA,USA:ICML:873-880.
Cui X Q,Tian Y,Weng L B and Yang Y P.2014.Anomaly detection in hyperspectral imagery based on low-rank and sparse decomposition//Proceedings of SPIE Volume 9069,Fifth International Conference on Graphic and Image Processing.Hong Kong,China:SPIE:90690R[DOI:10.1117/12.2050229]
Du P J,Xia J S,Xue C H,Tan K,Su H J and Bao R.2016.Review of hyperspectral remote sensing image classification.Journal of Remote Sensing,20(2):236-256(杜培军,夏俊士,薛朝辉,谭琨,苏红军,鲍蕊.2016.高光谱遥感影像分类研究进展.遥感学报,20(2):236-256)[DOI:10.11834/jrs.20165022]
Kwon H,Der S Z and Nasrabadi N M.2003.Adaptive anomaly detection using subspace separation for hyperspectral imagery.Optical Engineering,42(11):3342-3351[DOI:10.1117/1.1614265]
Li W and Du Q.2015.Collaborative representation for hyperspectral anomaly detection.IEEE Transactions on Geoscience and Remote Sensing,53(3):1463-1474[DOI:10.1109/TGRS.2014.2343955]
Lin Z,Ganesh A,Wright J,Wu L,Chen M and Ma Y.2009.Fast convex optimization algorithms for exact recovery of a corrupted lowrank matrix.Proceedings in International workshops on Computational Advances in Multi-Sensor Adaptive Processing(CAMSAP),1-18[DOI:10.1.1.231.4169]
Lin Z C,Chen M M and Ma Y.2010.The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices.ar Xiv:1009.5055
Liu G C,Lin Z C,Yan S C,Sun J,Yu Y and Ma Y.2013.Robust recovery of subspace structures by low-rank representation.IEEETransactions on Pattern Analysis and Machine Intelligence,35(1):171-184[DOI:10.1109/TPAMI.2012.88]
Liu W M and Chang C I.2013.Multiple-window anomaly detection for hyperspectral imagery.IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing,6(2):644-658plied Earth Observations and Remote Sensing,6(2):644-658[DOI:10.1109/JSTARS.2013.2239959]
Nasrabadi N M.2014.Hyperspectral target detection:an overview of current and future challenges.IEEE Signal Processing Magazine,31(1):34-44[DOI:10.1109/MSP.2013.2278992]
Rahmani M and Atia G.2015.Randomized robust subspace recovery for high dimensional data matrices.ar Xiv:1505.05901
Reed I S and Yu X.1990.Adaptive multiple-band CFAR detection of an optical pattern with unknown spectral distribution.IEEE Transactions on Acoustics,Speech,and Signal Processing,38(10):1760-1770[DOI:10.1109/29.60107]
Sun W W,Liu C,Li J L,Lai Y M and Li W Y.2014.Low-rank and sparse matrix decomposition-based anomaly detection for hyperspectral imagery.Journal of Applied Remote Sensing,8(1):083641[DOI:10.1117/1.JRS.8.083641]
Sun W W,Yang G,Du B,Zhang L F and Zhang L P.2017.A sparse and low-rank near-isometric linear embedding method for feature extraction in hyperspectral imagery classification.IEEE Transactions on Geoscience and Remote Sensing,55(7):4032-4046[DOI:10.1109/TGRS.2017.2686842]
Tong Q X,Zhang B and Zhang L F.2016.Current progress of hyperspectral remote sensing in China.Journal of Remote Sensing,20(5):689-707(童庆禧,张兵,张立福.2016.中国高光谱遥感的前沿进展.遥感学报,20(5):689-707)[DOI:10.11834/jrs.20166264]
Wang Y M,Jia J X,He Z P and Wang J Y.2016.Key technologies of advanced hyperspectral imaging system.Journal of Remote Sensing,20(5):850-857(王跃明,贾建鑫,何志平,王建宇.2016.若干高光谱成像新技术及其应用研究.遥感学报,20(5):850-857)[DOI:10.11834/jrs.20166206]
Wu Z B,Li Y L,Plaza A,Li J,Xiao F and Wei Z H.2016.Parallel and distributed dimensionality reduction of hyperspectral data on cloud computing architectures.IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing,9(6):2270-2278[DOI:10.1109/JSTARS.2016.2542193]
Xu H,Caramanis C and Sanghavi S.2010.Robust PCA via outlier pursuit//Proceedings of the 23rd International Conference on Neural Information Processing Systems.Vancouver,British Columbia,Canada:Curran Associates Inc.:2496-2504
Xu Y,Wu Z B,Li J,Plaza A and Wei Z H.2016.Anomaly detection in hyperspectral images based on low-rank and sparse representation.IEEE Transactions on Geoscience and Remote Sensing,54(4):1990-2000[DOI:10.1109/TGRS.2015.2493201]
Zhang L P,Du B and Zhong Y F.2010.Hybrid detectors based on selective endmembers.IEEE Transactions on Geoscience and Remote Sensing,48(6):2633-2646[DOI:10.1109/TGRS.2010.2040284]
Zhang L P and Li J Y.2016.Development and prospect of sparse representation-based hyperspectral image processing and analysis.Journal of Remote Sensing,20(5):1091-1101(张良培,李家艺.2016.高光谱图像稀疏信息处理综述与展望.遥感学报,20(5):1091-1101)[DOI:10.11834/jrs.20166050]
Zhang Y X,Du B and Zhang L P.2015.A sparse representation-based binary hypothesis model for target detection in hyperspectral images.IEEE Transactions on Geoscience and Remote Sensing,53(3):1346-1354[DOI:10.1109/TGRS.2014.2337883]
Zhao R,Du B and Zhang L P.2014.A robust nonlinear hyperspectral anomaly detection approach.IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing,7(4):1227-1234[DOI:10.1109/JSTARS.2014.2311995]