Anomaly detection is an active topic in hyperspectral image processing. Recently, low-rank representation (LRR)-based approaches have shown satisfactory results in wide anomaly detection applications. However, the existing LRR methods still have the following two problems: 1) setting a fixed value as a termination condition of the iterative constraint often results in the loss of target information, leading to a low detection rate with some missing targets, and 2) noise after LRR still remains in the sparse part, which increases false alarms. This article proposes the tensor approximation with LRR and the kurtosis correlation constraint (TAKCC) method for anomaly detection. The hyperspectral image is regarded as a third-order tensor for the LRR process. In the optimization process, the background suppression degree is obtained through the background dictionary to determine the iteration termination condition. After the iterative optimization is completed, the low-rank tensor that can fully represent the background is obtained. Also, the difference between the original hyperspectral image tensor and the low-rank tensor is used as the input of the kurtosis correlation constraint. The kurtosis correlation constraint compares the similarity between the current pixel and its surrounding pixels to detect the anomaly, where the kurtosis in the high-order statistical feature is introduced to avoid the interference of noise. The experimental results illustrate that the proposed method can retain the complete target information to highlight targets while suppressing background.

中文翻译：

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具有低秩表示和峰度相关约束的张量逼近用于高光谱异常检测

异常检测是高光谱图像处理中的一个活跃话题。最近，基于低秩表示（LRR）的方法在广泛的异常检测应用中显示出令人满意的结果。但是，现有的LRR方法仍然存在以下两个问题：1）设置一个固定值作为迭代约束的终止条件，往往会导致目标信息的丢失，导致部分目标缺失的检测率低；2） LRR 后的噪声仍然留在稀疏部分，这增加了误报。本文提出了使用 LRR 的张量逼近和峰度相关约束 (TAKCC) 方法进行异常检测。高光谱图像被视为 LRR 过程的三阶张量。在优化过程中，通过背景字典得到背景抑制度，确定迭代终止条件。迭代优化完成后，得到能完全代表背景的低秩张量。此外，原始高光谱图像张量与低秩张量之间的差异用作峰态相关约束的输入。峰度相关约束通过比较当前像素与其周围像素的相似度来检测异常，其中引入了高阶统计特征中的峰度以避免噪声的干扰。实验结果表明，该方法可以保留完整的目标信息，在抑制背景的同时突出目标。