Hyperbolic Space-Based Autoencoder for Hyperspectral Anomaly Detection

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.