Deep-learning (DL)-based methods have been shown to be effective on the hyperspectral image (HSI) anomaly detection task because of their feature extraction ability. However, current DL-based methods lack an effective means of regularizing the background information. In this article, the hyperbolic space-based autoencoder (HSAE) is proposed for the hyperspectral anomaly detection task. We assume that an effective hierarchical structural representation can better model the HSI in the spatial domain, and this enables the background information to be effectively regularized. Motivated by this idea, the HSAE embeds the HSI into hyperbolic space, which is a non-Euclidean geometry with a constant negative curvature and an exponential growth distance between points. Using a wrapped normal prior distribution, the training of the hidden representation is supervised to preserve more hierarchical features. After the training process, a hyperbolic distance-based anomaly detector (HDB) is introduced to discover anomalies in a more robust way. Experimental results on several popular HSI benchmarks fully demonstrate the superiority of our HSAE.

中文翻译：

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用于高光谱异常检测的双曲空间自动编码器


基于深度学习（DL）的方法因其特征提取能力而被证明在高光谱图像（HSI）异常检测任务中是有效的。然而，当前基于深度学习的方法缺乏有效的手段来规范背景信息。在本文中，提出了基于双曲空间的自动编码器（HSAE）用于高光谱异常检测任务。我们假设有效的层次结构表示可以更好地在空间域中对 HSI 进行建模，这使得背景信息能够得到有效的正则化。受此想法的启发，HSAE 将 HSI 嵌入到双曲空间中，双曲空间是一种具有恒定负曲率和点之间指数增长距离的非欧几里得几何。使用包装正态先验分布，对隐藏表示的训练进行监督以保留更多层次特征。训练过程结束后，引入基于双曲距离的异常检测器（HDB）以更稳健的方式发现异常。在几个流行的 HSI 基准上的实验结果充分证明了我们的 HSAE 的优越性。