Weighted-RXD and Linear Filter-Based RXD: Improving Background Statistics Estimation for Anomaly Detection in Hyperspectral Imagery

Anomaly detection is an active topic in hyperspectral imaging, with many practical applications. Reed-Xiaoli detector (RXD), a widely used method for anomaly detection, uses the covariance matrix and mean vector to represent background signals, assuming that the background information adjusts to a multivariate normal distribution. However, in general, real images present very complex backgrounds. As a result, in many situations, the background information cannot be properly modeled. An important reason is that that background samples often contain also anomalous pixels and noise, which lead to a high false alarm rate. Therefore, the characterization of the background is essential for successful anomaly detection. In this paper, we develop two novel approaches: weighted-RXD (W-RXD) and linear filter-based RXD (LF-RXD) aimed at improving background in RXD-based anomaly detection. By reducing the weight of the anomalous pixels or noise signals and increasing the weight of the background samples, W-RXD can provide better estimations of the background information. In turn, LF-RXD uses the probability of each pixel as background to filter wrong anomalous or noisy instances. Our experimental results, intended to analyze the performance of the newly developed anomaly detectors, indicate that the proposed approaches achieve good performance when compared with other classic approaches for anomaly detection in the literature.