Real-Time Recursive Hyperspectral Sample Processing for Passive Target Detection: Anomaly Detection

Abstract

In Chap. 5, a particular subtarget detection technique in active hyperspectral target detection, called constrained energy minimization (CEM), was developed for its real-time and causal implementation. Rather than CEM, this chapter focuses on passive hyperspectral target detection and investigates a commonly used passive target detection technique, anomaly detection (AD), especially for real-time and causal processing capabilities that are developed for CEM in Chap. 5 and will also be derived in a similar manner for AD. To this end, this chapter can be considered a companion chapter of Chap. 5. Technically speaking, passive target detection must be carried out without any prior knowledge, specifically, a complete lack of availability of target knowledge. Owing to the nature of hyperspectral imaging sensors, which can uncover many unknown material substances, passive hyperspectral target detection is a major task in hyperspectral image analysis and has been studied extensively in the literature. Applications of passive target detection include surveillance and monitoring, where no knowledge is required a priori. Of particular interest in passive target detection is AD, which is generally performed in a completely blind environment. To suppress unknown backgrounds, AD makes use of the global sample correlation/covariance matrix R/K, referred to as R/K-AD, so as to enhance its detectability. In general, anomalies appear unexpectedly and cannot be detected by visual inspection. Most importantly, they vary with time and data sample vectors. Accordingly, developing real-time processing for R/K-AD on a timely basis sample by sample is crucial and critical in many real-world applications, for example, abnormalities in agriculture and forestry, environmental monitoring, combat vehicles on a battlefield, drug trafficking in law enforcement, and food inspection. As noted in Chap. 5, this real-time process requires that causality be included in an algorithm’s design. In analogy with real-time CEM, the concept of a causal sample correlation matrix (CSCRM), introduced in Chap. 5, is also applicable to AD for this purpose. However, in a broader sense, CSCRM is expanded into a causal sample correlation/covariance matrix (CSCRM/CSCVM) to replace R/K with CSCRM/CSCVM specified by R(r n )/K(r n ), respectively, where r n is the current data sample vector being processed. The capability for real-time processing is then derived from such a CSCRM/CSCVM because CSCRM/CSCVM varies with data sample vectors. Thus, a causal processing of K-AD/R-AD requires repeatedly calculating inverses of such sample-varying CSCRM/CSCVM and must be processed in a causal manner sample by sample, referred to as causal K-AD/R-AD (CR-K-AD/CR-AD). To further reduce computational complexity and computer processing time for CK-AD/CR-AD, the notion of innovation in a Kalman filter developed in Chap. 3 is once again used to derive recursive causal update equations to calculate CSCRM/CSCVM, which leads to recursive versions of K-AD/R-AD, to be called recursive CK-AD/CR-AD (R-CK-AD/R-CR-AD). In particular, when R-CK-AD/R-CR-AD is realized by real-time processing, it is referred to as RT CK-AD/RT-CR-AD in this chapter.