Hyperspectral Anomaly Detection: A Dual Theory of Hyperspectral Target Detection

Hyperspectral target detection (HTD) and hyperspectral anomaly detection (HAD) are designed by completely different functionalities in terms of how to carry out target detection. Specifically, HTD is a reconnaissance technique looking for known targets as opposed to HAD which is a surveillance technique seeking unknown targets of interest. So, HTD is generally designed by the hypothesis testing theory to derive likelihood ratio test (LRT)-based detectors. However, such hypothesis testing theory-based HTD requires the targets under the alternative hypothesis to be known. In addition, it also requires knowledge of the probability distribution under each hypothesis such as Gaussian distributions. Accordingly, the LRT-based HTD cannot be directly applied to HAD. This article develops a dual theory of LRT-based HTD for HAD, which converts HTD to HAD by making LRT-based detectors anomaly detectors. In addition, by virtue of this dual theory a new signal-to-noise ratio (SNR)-based theory can be also developed for HAD. Interestingly, the commonly used hyperspectral anomaly detector, referred to as Reed and Xiaoli detector (RXD), which is derived from the generalized LRT (GLRT), can be also rederived by this dual theory as well as the new developed SNR-based HAD theory.