粗定位和协同表示的高光谱图像异常检测

目的 由于在军事和民用应用中的重要作用，高光谱遥感影像异常检测在过去的20~30年里一直都是备受关注的研究热点。然而，考虑到异常点往往藏匿于大量的背景像元之中，且只占据很少的数量，给精确检测带来了不小的挑战。针对此问题，基于异常点往往表现在高频的细节区域这一前提，本文提出了一种基于异常点粗定位和协同表示的高光谱遥感影像异常检测算法。方法 对输入的原始高光谱遥感影像进行空间维的降质操作；通过衡量降质后影像与原始影像在空间维的差异，粗略定位可能的异常点位置；将粗定位的异常点位置用于指导像元间的协同表示以重构像元；通过衡量重构像元与原始像元的差异，从而进一步优化异常检测结果。结果 在4个数据集上与6种方法进行了实验对比。对于San Diego数据集，次优算法和本文算法分别取得的AUC （area under curve）值为0.978 6和0.994 0；对于HYDICE （hyperspectral digital image collection equipment）数据集，次优算法和本文算法的AUC值为0.993 6和0.998 5；对于Honghu数据集，次优算法和本文方法的AUC值分别为0.999 2和0.999 3；对Grand Isle数据集而言，尽管本文方法以0.001的差距略低于性能第1的算法，但从目视结果图中可见，本文方法所产生的虚警目标远少于性能第1的算法。结论 本文所提出的粗定位和协同表示的高光谱异常检测算法，综合考虑了高光谱遥感影像的谱间特性，同时还利用了其空间特性以及空间信息的先验分布，从而获得异常检测结果的提升。

Rough location and collaborative representation for hyperspectral image anomaly detection

Objective Hyperspectral image has rich spectral information. Different materials correspond to different spectral information, which can be applied to disaster warning, agriculture precision, and authenticity identification for some valuable art works. Anomaly detection of hyperspectral images refers to detecting the anomalous pixels in the scene without any prior information, and it is important in military and civil applications. In this way, the anomaly detection of hyperspectral images has gained increasing popularity. The anomalies usually refer to the outliers with spatial and spectral signatures that are severely different from their surroundings. Compared with the background, the anomalies have two main characteristics. First, their spectral information is severely different from that of their surroundings, and this phenomenon is named the spectral difference. Meanwhile, the anomalies are usually embedded into the local homogeneous background in a format of several pixels or even sub-pixels, and this phenomenon is called the spatial difference. Anomalies are often hidden in a large number of background pixels, and they only occupy a small number. Thus, they bring a great challenge to accurate detection. This study proposes a hyperspectral anomaly detection algorithm based on rough localization and collaborative representation of outliers to solve this problem. It is based on the institution that the anomalies often appear in high-frequency detail areas. Method A novel hyperspectral anomaly detection method based on the rough location and collaborative representation is proposed in this study. This method utilizes the spatial information and inter-spectral information carried by the hyperspectral images simultaneously, which ensures the accuracy of the algorithm. Three modules are included in the whole detection process. First, the original hyperspectral image is degraded in spatial dimension. Second, we can obtain the rough response map of spatial anomaly by measuring the difference between the degraded and original images in spatial dimension and locate the possible abnormal points according to the response value considering that the degradation operation of spatial dimension often loses high-frequency information. Finally, the rough location of outliers is used to guide the collaborative representation between pixels for reconstructing the center pixel. The detection result is further optimized by measuring the difference between the reconstructed center and original pixels. Experimental data contain four real-scenario datasets, namely, the San Diego, Grand Isle, hyperspectral digital image collection equipment(HYDICE), and Honghu datasets. Experimental results demonstrate the effectiveness of the proposed method. Experimental comparison is made with six classical methods, namely, the Global-RX(Reed-Xiaoli) detector (RXD), Local-RX detector (LRX), collaborative representation-based detector (CRD), tensor completion-based detector (TCD), fractional Fourier estimation (FrFE), and low-rank and sparse decomposition model with mixture of Gaussian (LSDM-MoG). The FrFE detector utilizes the fractional Fourier transformation to the spectral information, and it obtains the optimal order and the corresponding spectral feature. The spectral feature is further detected by the Reed-Xiaoli(RX) detector. In this way, the RXD, LRX, and the FrFE all belong to the statistical-based detectors. LSDM-MoG imports the mixture of Gaussian as a regularization term for the low-rank and sparse decomposition model, which is a typical representation-based anomaly detection method. In this way, the CRD, TCD, and the LSDM-MoG all belong to the representation-based detectors. Result We incorporate four real-scenario hyperspectral images to validate the performance of the proposed method. The quantitative evaluation metrics include the receiver operating curves and the area under the curve (AUC) value to evaluate the detection accuracy. Meanwhile, we also exhibit the detection maps of each method for visual comparison. The average results of the three datasets indicate that the second optimal mean AUC value (0.992 4) is achieved by the CRD detector. The corresponding mean AUC value achieved by the proposed method is 0.997 3. Compared with the algorithm with the second best performance, the AUC value for the San Diego dataset is increased from 0.978 6 to 0.994 0 by the proposed method. For the HYDICE dataset, the AUC value is increased from 0.996 3 to 0.998 5 by the proposed method compared with the detector with the second best performance. For the Honghu dataset depicting a long river bank in Honghu, Hubei Province of China, the proposed method achieves the AUC value of 0.999 3, which is superior than that of the detector with the second best performance. For the Grand Isle dataset, the AUC value of the proposed detector is slightly lower than that of the LSDM-MoG detector with the optimal performance by a gap of 0.001. However, the visual maps reveal that the false alarm targets generated by the LSDM-MoG are more frequent than those of the proposed method. Experimental results and data analysis demonstrate the effectiveness of the proposed algorithm. Conclusion A rough detection and collaborative representation-based algorithm for anomaly detection of hyperspectral images is proposed in this study. The anomalous and background pixels are coarsely separated by a simple spatial degradation processing. Meanwhile, the coarsely separated background and anomaly response map is utilized to guide the locally collaborative representation between pixels. Purer background characteristics can be expressed with the guidance of the rough detection map, and the suppression of anomalous pixels due to the polluted background in the detection process is avoided. Accordingly, the detection accuracy is improved. Meanwhile, parameters in the collaborative representation process decrease with the reduction in participating elements. Over-fitting phenomenon is unlikely to be produced with the simpler optimization model, which ensures the effectiveness of the algorithm. In this way, the proposed method utilizes not only the spectral characteristics of hyperspectral images but also their spatial characteristics and the prior information of spatial information. Experimental results and comparative analysis demonstrate the effectiveness of the proposed method in anomaly detection.