为提高高光谱图像异常目标检测的精度,提出一种基于拉普拉斯矩阵图的异常目标检测方法(Laplacian Matrix Graph for Anomaly Detection,LGD)。通过构造全连接图和高斯核函数构造的近邻矩阵,将高光谱图像中异常目标的位置和光谱信息进行联合处理,实现了高光谱数据不同波段之间的信息融合;利用图的傅里叶变换和拉普拉斯矩阵性能,将图信号的总变差作为判断异常目标的评价函数,实现了异常目标像素点的准确检测,避免了常规检测算法中的矩阵求逆问题,降低了算法的复杂度。在异常检测常用的AVIRIS-I、AVIRIS-II、ABU-urban-2、ABU-urban-4和EI Segundo 5种高光谱数据集上,进行了算法性能验证。实验结果表明:该算法在5种数据集上异常目标检测的AUC值与ROC曲线均优于其他算法,在检测精度上具有明显优势。
This paper studies the problem of the spectral radius of the uniform hypergraph determined by the signless Laplacian matrix.The upper bound of the spectral radius of a uniform hypergraph is obtained by using Rayleigh principle and the perturbation of the spectral radius under moving the edge operation,and the extremal hypergraphs are characterized for both supertree and unicyclic hypergraphs.The spectral radius of the graph is generalized.
