Real-Time Recursive Hyperspectral Sample Processing for Active Target Detection: Constrained Energy Minimization

Abstract

As discussed in Chap. 5 of Chang (Real-time progressive hyperspectral image processing: endmember finding and anomaly detection, Springer, New York, 2016) hyperspectral target detection can be generally performed in two completely opposite modes, active hyperspectral target detection and passive hyperspectral target detection. Active hyperspectral target detection requires specific prior knowledge that can be used to detect targets of interest as desired objects. Its applications include reconnaissance, rescue and search, and detection of targets specified by known knowledge. In the meantime, target detection of this type generally requires real-time processing to find targets on a timely basis. However, for an algorithm to be implemented in real time, the data samples used can only be those data sample vectors up to the data sample currently being processed; no future data sample vectors yet to be visited should be involved in data processing. Such a property is generally called causality, which has unfortunately received little attention in real-time hyperspectral data processing in recent years. This chapter investigates one of the well-known active hyperspectral target detection techniques, constrained energy minimization (CEM), for its real-time processing in subpixel detection. In this investigation, the concept of causal sample correlation matrix (CSCRM), introduced in Chap. 14 in Chang (Real-time progressive hyperspectral image processing: endmember finding and anomaly detection, Springer, New York, 2016), will play a key role in allowing CEM to be implemented in a progressive manner sample by sample. Such resulting CEM is called progressive CEM (P-CEM). Because CSCRM varies with data sample vectors, P-CEM requires repeatedly calculating the inverses of such sample-varying CSCRM matrices. To further reduce computational complexity and computer processing time, the notion of innovation developed in Chap. 3 for a Kalman filter is used to derive recursive equations for P-CEM. The resultant recursive version of P-CEM is referred to as recursive CEM (R-CEM), which paves the way to developing real-time constrained energy minimization (RT-CEM), which can be executed in a causal manner recursively as well as in real-time sample by sample progressively.