Real-time causal processing of anomaly detection
Yulei Wang, Shih-Yu Chen, Chao-Cheng Wu, Chunhong Liu, Chein‐I Chang · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2012
Anomaly detection generally requires real time processing to find targets on a timely basis. However, for an algorithm to be a real time processing it can only use data samples up to the sample currently being visited and no future data samples can be used for data processing. Such a property is generally called “causality”, which has unfortunately received little interest in the past. Recently, a causal anomaly detector derived from a well-known anomaly detector, called RX detector, referred to as causal RXD (C-RXD) was developed for this purpose where the sample covariance matrix, K used in RXD was replaced by the sample correlation matrix, R(n) which can be updated up to the currently being visited data sample, rn. However, such proposed C-RXD is not a real processing algorithm since the inverse of the matrix R(n), R-1(n) is recalculated by entire data samples up to rn. In order to implement C-RXD the matrix R(n) must be carried out in such a fashion that the matrix R-1(n) can be updated only through previously calculated R-1(n-1) as well as the currently being processed data sample rn. This paper develops a real time processing of CRXD, called real time causal anomaly detector (RT-C-RXD) which is derived from the concept of Kalman filtering via a causal update equation using only innovations information provided by the pixel currently being processed without re-processing previous pixels.