伴随高光谱图像的广泛使用, 高光谱图像技术得到长足的发展, 其中高光谱图像异常检测技术越发受到重视。 为了解决传统高光谱图像异常检测技术的实用性和检测效果不佳的问题, 提出一种新颖的低秩表示检测算法。 对于高光谱图像, 大部分背景像元均可以被少量主要的背景像元组合近似地表示, 且它们的表示系数将会位于低秩的空间中。 在剩下无法被主要背景像元表示的稀疏部分中存在着异常像元, 则可以被检测算法提取出来。 在低秩表示中, 背景像元字典的构建将会影响高光谱图像中背景像元的表示。 如直接从现有高光谱图像中提取背景像元构建字典, 会导致异常像元对背景像元字典的污染。 而利用待检测高光谱图像观测数据和由光谱组成原理可合成的潜在未观测数据来构建背景像元字典, 提取出背景像元的主要特征, 有利于更好地分离出稀疏异常像元的信息。 并且高光谱图像数据存在高维几何结构特点, 通过引入拉普拉斯矩阵来约束空间中局部相似的像元对于待检测像元的表示作用, 获得更接近于真实的表示系数。 实验结果分别在仿真数据和真实数据上验证, 与传统方法相比, 提出的方法通过有效地突出异常像元提高了检出率和抑制了背景像元, 降低了误检率。

With the widespread use of hyperspectral images, hyperspectral image technology has made considerable progress, of which hyperspectral image anomaly detection technology has received more and more attention. In order to solve the problem of poor practicability and poor detection effect of traditional hyperspectral image anomaly detection techniques, this paper presents a novel low rank representation detection algorithm. For hyperspectral images, most of the background pixels can be approximated by a small number of major background pixel combinations, and their representation coefficients will be located in a low-rank space. While the remaining anomalous pixels in the sparse part that can not be represented by the main background pixels can be extracted by the detection algorithm. In low-rank representations, the construction of the background pixel dictionary will affect the representation of the background pixels in the hyperspectral image. When extracting the background pixels directly from the existing hyperspectral image to construct the dictionary, this process will lead to the contamination of the background pixel dictionary by the abnormal pixels. So in this paper, the background pixel dictionary is constructed by using the observed data on the hyperspectral image to be detected and the potential unobserved data that can be synthesized by the principle of spectral composition, and the main features of the background pixels are extracted, helping to better separate the sparse anomalous pixel Information. Hyperspectral image data is characterized by high-dimensional geometry. In this paper, we introduce a Laplacian matrix to constrain the representation of locally similar pixels in the space to be detected, and get a closer representation of the true representation coefficients. The experimental results are validated respectively on the simulation data and the real data, showing that the proposed method reduces the false detection rate by effectively highlighting the abnormal pixels and improves the detection rate by suppressing the background pixels.