LREN: Low-Rank Embedded Network for Sample-Free Hyperspectral Anomaly Detection

Hyperspectral anomaly detection (HAD) is a challenging task because it explores the intrinsic structure of complex highdimensional signals without any samples at training time. Deep neural networks (DNNs) can dig out the underlying distribution of hyperspectral data but are limited by the labeling of large-scale hyperspectral datasets, especially the low spatial resolution of hyperspectral data, which makes labeling more difficult. To tackle this problem while ensuring the detection performance, we present an unsupervised lowrank embedded network (LREN) in this paper. LREN is a joint learning network in which the latent representation is specifically designed for HAD, rather than merely as a feature input for the detector. And it searches the lowest rank representation based on a representative and discriminative dictionary in the deep latent space to estimate the residual efficiently. Considering the physically mixing properties in hyperspectral imaging, we develop a trainable density estimation module based on Gaussian mixture model (GMM) in the deep latent space to construct a dictionary that can better characterize the complex hyperspectral images (HSIs). The closed-form solution of the proposed low-rank learner surpasses existing approaches on four real hyperspectral datasets with different anomalies. We argue that this unified framework paves a novel way to combine feature extraction and anomaly estimation-based methods for HAD, which intends to learn the underlying representation tailored for HAD without the prerequisite of manually labeled data. Code available at https://github.com/xdjiangkai/LREN.