高光谱遥感技术是遥感领域的一次突破，高光谱遥感图像可以看作一个图像立方体，具有光谱分辨率高、图谱合一的特点，且含有丰富的空谱信息。高光谱异常检测作为目标探测的一个分支，不依赖任何先验知识，因此在环境监测、精准农林和国防军事等领域发挥着越来越重要的作用。异常检测是一个二分类问题，其目的是在没有先验知识的情况下检测出与大量背景像元存在光谱差异且在空间上分布稀疏的像元。高光谱图像可以提供地物丰富的空谱信息，研究表明利用空间信息有助于进一步提高异常检测的可靠性和稳定性。本文结合高光谱影像的特点，充分利用高光谱图像的空谱信息，提出基于空谱信息联合的高光谱图像异常检测算法，研究内容分为三部分：

    （1）针对协同表示周围的像元存在异常污染、没有充分利用空间信息等问题，本文将空间-光谱相结合，提出了基于背景净化和局部空间相似性的高光谱异常检测方法。首先采用经典的最小二乘法对局部窗口内的背景像元进行纯化，选取较为纯净的背景像元进行协同表示；然后通过局部空间相似度计算出局部空间异常值；最后对光谱和空间异常值进行融合得到最终结果。在四个高光谱数据上进行实验验证，结果表明本文方法具有更高的检测精度与更低的虚警率。

    （2）针对基于低秩稀疏表示的异常检测方法中背景字典易受污染、空间信息利用不足等问题，本文提出了一种基于聚类空谱背景字典的低秩稀疏表示高光谱异常检测方法。首先利用图像的空谱信息对低秩稀疏表示算法中的字典构造方式进行改进，构造的字典由背景像素组成，并且包含了所有背景类；然后使用低秩稀疏表示算法对高光谱图像进行重构，重构残差越大，属于异常的可能性越大。实验结果表明，四组数据集上的AUC（Area Under the ROC Curve）值均在0.98以上，证明该方法能够有效地提升检测精度。

    （3）针对异常检测大多数方法未有效保留原始高光谱数据的三维结构、空间分辨率低以及噪声大等问题，本文将特征提取和背景净化相结合，提出了基于低秩平滑约束张量分解和特征提取的高光谱异常检测方法。首先将不同的先验加入到不同的张量维度中，对其不断优化迭代分解为背景张量和异常张量；其次对高光谱数据进行分数阶傅里叶变换从而增大异常和目标之间的差异，且此变换能有效去除噪声；最后将得到的背景张量和经过分数阶傅里叶变换得到的图像进行基于马氏距离的检测。实验结果表明本文所提方法的AUC值相比其它五种经典方法有所提高，能有效地将背景和目标分离，具有较高的检测精度。

        Hyperspectral remote sensing technology is a breakthrough in the field of remote sensing. Hyperspectral remote sensing images can be regarded as an image cube, characterized by high spectral resolution, unity of maps, and containing rich spatial information. Hyperspectral anomaly detection, as a branch of target detection, does not rely on any a priori knowledge, and therefore plays an increasingly important role in the fields of environmental monitoring, precision agriculture and forestry, and national defense and military. Anomaly detection is a binary classification problem, which aims to detect spectrally different and sparsely spatially distributed image elements from a large number of background image elements without a priori knowledge. Hyperspectral images can provide rich spatial-spectral information of features, and studies have shown that utilizing spatial information helps to further improve the reliability and stability of anomaly detection. Combined with the characteristics of hyperspectral images, this paper makes full use of the space spectrum information of hyperspectral images, and proposes an anomaly detection algorithm based on the combination of space spectrum information. The research content is divided into three parts:

(1) Aiming at the problems of anomalous contamination of the image elements around the cooperative representation and not fully utilizing the spatial information, this paper combines the spatial-spectral combination and proposes a hyperspectral anomaly detection method based on the background purification and local spatial similarity. Firstly, the classical least squares method is used to purify the background pixels in the local window, and the purer background pixels are selected for the cooperative representation; then the local spatial anomalies are calculated by the local spatial similarity; finally, the spectral and spatial anomalies are fused to obtain the final results. The experimental validation is carried out on four hyperspectral data, and the results show that the method in this paper has higher detection accuracy and lower false alarm rate.

(2) Aiming at the problems of easy contamination of the background dictionary and insufficient utilization of spatial information in the anomaly detection method based on low-rank sparse representation, this paper proposes a low-rank sparse representation hyperspectral anomaly detection method based on clustered null-spectrum background dictionary. The dictionary construction method in the low-rank sparse representation algorithm is improved by utilizing the null spectral information of the image, and the constructed dictionary consists of background pixels and contains all the background classes; then the hyperspectral image is reconstructed using the LRASR algorithm, and the larger the reconstruction residual is, the higher the probability of belonging to the anomaly is. The experimental results show that the AUC values on the four datasets are above 0.98, proving that the method can effectively improve the detection accuracy.

(3) Aiming at the problems that most of the anomaly detection methods do not effectively retain the three-dimensional structure of the original hyperspectral data, have low spatial resolution, and are noisy, this paper proposes a hyperspectral anomaly detection method based on low-rank smoothing constrained tensor decomposition and feature extraction by combining the feature extraction and background purification. Firstly, different a priori are added to different tensor dimensions, which are continuously optimized and iteratively decomposed into background tensor and anomaly tensor, secondly, the hyperspectral data are subjected to fractional-order Fourier transform so as to increase the difference between the anomaly and the target, and this transform can effectively remove the noise, and finally, the background tensor and the image obtained by fractional-order Fourier transform are subjected to the detection based on the Mahalanobis distance. The experimental results show that the AUC value of the proposed method is improved compared with the other five classical methods, which can effectively separate the background and the target with high detection accuracy.

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