Real-time causal processing of anomaly detection for hyperspectral imagery

Anomaly detection generally requires real-time processing to find targets on a timely basis. However, for an algorithm to be implemented in real time, the used data samples can be only those up to the data sample being visited; no future data samples should be involved in the data processing. Such a property is generally called causality, which has unfortunately received little interest thus far in real-time hyperspectral data processing. This paper develops causal processing to perform anomaly detection that can be also implemented in real time. The ability of real-time causal processing is derived from the concept of innovations used to derive a Kalman filter via a recursive causal update equation. Specifically, two commonly used anomaly detectors, sample covariance matrix (K)-based Reed-Xiaoli detector (RXD), called K-RXD, and sample correlation matrix (R)-based RXD, called R-RXD, are derived for their real-time causal processing versions. To substantiate their utility in applications of anomaly detection, real image data sets are conducted for experiments.