基于空间密度聚类的改进KRX高光谱异常检测

高光谱遥感影像包含了丰富的光谱信息，对于地物具有极强的分辨能力，从而促进了不需任何先验信息的高光谱异常目标探测技术的发展。KRX（Kernel RX）异常探测算法巧妙地利用核函数将RX算法映射至高维特征空间，加强了光谱中非线性信息的运用，具有较强的可分辨性，显著改善了低维空间的光谱不可分问题。然而，也暴露了KRX算法中病态Gram矩阵求逆误差大，异常检测效率低等缺点。为实现理论上KRX算法的强探测性能，提出一种基于新型聚类方法的改进KRX探测算法（DC-KRX）。（1）由于空间邻域像元具有较强的光谱相似性，会造成Gram矩阵病态，严重影响了异常探测效果，因此背景虚检现象严重。针对病态Gram矩阵的求逆误差问题，算法改进了KRX算子，对Gram矩阵进行奇异值分解，选取特征值较大的主成分，保证了Gram矩阵的求逆精度，待测像元的探测结果采用l-2范数表示，检测效果提高明显；（2）在改进KRX的基础上，提出了空间聚类KRX算法。空间像元之间具有光谱强相关性，既造成了Gram矩阵的病态，数据的冗余也影响了探测效率。实验发现，通过聚类算法可以合并像元于聚类中心，减少空间维度，提高计算效率；同时，聚类中心按照聚类大小被赋予不同的权重，保证了探测精度；（3）另一方面，选用合适的聚类算法是一个难点。聚类KRX算法对于聚类算法的精度和实时性要求较高，比较发现，一种基于密度峰值快速搜索（DC）的新型聚类算法具有较好的聚类性能。算法采用欧式距离计算任意像元的相似度，利用局部密度和邻域距离作为聚类中心的联合判断准则，对结果进行排序得到聚类中心。实验发现，该聚类算法计算速度快，且能够对任意形状的分布进行聚类，非常适合于维度较高，成分复杂的高光谱图像，且适用于较高次数的重复聚类。DC-KRX算法提供了一种空间聚类预处理的高光谱异常探测新思路，最后，与国际主流探测算法对比发现，该算法表现了较好的探测性能。同时，时效性对比分析发现，聚类前后算法的检测效率提高了30%以上，有效改善了KRX算法的实时性。

A Density-Based Cluster Kernel RX Algorithm for Hyperspectral Anomaly Detection

Hyperspectral remote sensing image contains abundant spectral information, which has strong ability to distinguish ground objects, thus promoting the development of hyperspectral anomaly detection technology without any prior information. Kernel-RX algorithm uses the kernel function to ably RX algorithm mapped to high-dimensional feature space, which has a strong ability to solve the spectrum inseparable problem in the low dimensional space. However, it also reveals the disadvantages such as large inverse error in ill-conditioned matrix and low efficiency. In order to realize the strong detection performance of KRX algorithm in theory, this paper proposes an improved KRX detection technology based on new clustering algorithm. (1) Due to the strong spectral similarity of spatial neighborhood pixels, the Gram matrix is ill-conditioned, which seriously affects the detection performance of anomalies, so the phenomenon of background error detection is serious. In order to solve the problem of the inverse error of ill-conditioned Gram matrix, the algorithm improves the KRX operator. By decomposing the singular value of Gram matrix and selecting the principal component with larger eigenvalue, the algorithm ensures the inverse accuracy of Gram matrix. In the end, the detection result of the pixel to be measured is expressed by l-2 norm. The experiment shows that the detection effect is improved obviously. (2) Based on the improved KRX, a spatial clustering KRX algorithm is proposed. There is strong a correlation between spatial pixels, which not only leads to the ill-condition of Gram matrix, but also affects the detection efficiency. The experimental results show that combining pixels in the clustercenters can reduce the spatial dimension and improve the computational efficiency. At the same time, the clustering center is given different weight factors according to the size of the cluster, which ensures the detection accuracy. (3) On the other hand, it is difficult to select an appropriate clustering algorithm. Clustering KRX algorithm requires high accuracy and real-time performance. It is found that a new clustering algorithm based on the peak density fast search algorithm has better clustering performance. The Euclidean distance is used to calculate the similarity of any two pixels, and the Local Density and Neighborhood Distance are used to calculate the clustering center. The clustering center is obtained by sorting the results of the Joint Judgement Criterion. The clustering results show that this clustering algorithm is fast and can cluster arbitrary shape distribution, which is very suitable for hyperspectral images with high dimension and complex components, and can be used for repeated clustering with high frequency of anomaly detection. In conclusion, DC-KRX algorithm provides a new idea of hyperspectral anomaly detection based on spatial clustering preprocessing. Finally, the algorithm is compared with the advanced method. The results show our method has a strong detection performance. And, it is found that the detection efficiency of clustering algorithm is improved by more than 30%, which greatly improves the real-time performance of KRX algorithm.