Recursive Hyperspectral Sample Processing of Automatic Target Generation Process

The automatic target generation process (ATGP) described in Sect. 4.4.2.3 is an active unsupervised subpixel target detection technique. It has been used in a wide range of applications in hyperspectral image analysis to find unknown targets and endmembers. Since it is a pixel-based technique, it can be very easily implemented in real time. In addition, because it is also unsupervised, it can be used to find unknown targets automatically without prior knowledge via a succession of orthogonal subspace projections (OSPs) to search for potential targets of interest in sequence. In this regard, ATGP is actually a progressive target detection technique in the sense that it finds one target at a time in real time and one target after another progressively. However, ATGP cannot be implemented as a real-time process to find all targets because ATGP repeatedly implements OSPs on growing subspaces, which are augmented by newly found targets one at a time. This process requires a significant amount of computing time, which will grow exponentially as the number of targets is increased. Another is that it does not have an automatic stopping rule to terminate the process in real time. This chapter develops a recursive version of ATGP, called recursive hyperspectral sample processing of ATGP (RHSP-ATGP), to address these two issues. By taking advantage of the fact that target subspaces are nested in a cascade in the sense that previous target subspaces are always embedded as part of subsequently generated target subspaces, RHSP-ATGP derives recursive equations to update current target subspaces without reprocessing previously generated target subspaces. As a result, it works as if it were a Kalman filter as a real-time processing algorithm. To terminate RHSP-ATGP in real time, a Neyman–Pearson detector based on target-specified virtual dimensionality, developed in Chap. 4, is further developed to test each target found by ATGP in real time to determine whether ATGP is to be terminated. This idea is similar to the Harsanyi–Farrand–Chang method used to estimate virtual dimensionality (VD) (Harsanyi et al. Annual meeting, proceedings of American society of photogrammetry and remote sensing, Reno, 236–247, 1994a; Chang Hyperspectral imaging: techniques for spectral detection and classification. Dordrecht: Kluwer Academic, 2003a; Chang and Du, IEEE Transactions on Geoscience and Remote Sensing 42:608–619, 2004).