31.3 Hyperspectral Imaging Techniques Expanded by BDE
In this section, three well-known HSI techniques, orthogonal subspace projection (OSP), constrained energy minimization (CEM), and RX-detector (RXD) described in Chapter 8 are considered as candidates to be expanded by BDE as MSI techniques. This is because each of these three techniques requires a different level of target knowledge. For OSP to work effectively, the complete knowledge of image endmembers including background must be provided a priori. Since such full target knowledge required by OSP is nearly impossible to obtain, specifically for image background, CEM is then developed to cope with this dilemma where only targets of interest are required to know in advance while the complete image background can be discarded. When obtaining partial knowledge of interesting targets becomes infeasible, RXD may be used to serve as this purpose for anomaly detection. In what follows, OSP, CEM, and RXD will be generalized to BEP-OSP, BEP-CEM, and BEP-RXD by including BEP as a preprocessing for BDE.
31.3.1 BEP-Based Orthogonal Subspace Projection
The BEP-based OSP introduced in this section operates in two phases. The first phase implements BEP to create additional new spectral bands from the original spectral bands. The objective of BEP is to make use of nonlinear correlation functions to produce a new set of second-order statistical bands. It is then followed by the second phase carried out by OSP. The procedure to implement the BEP-based orthogonal subspace projection (BEP-OSP) is summarized as follows:
Phase (1) Band Generation Process
Phase (2) OSP
31.3.2 BEP-Based Constrained Energy Minimization
In analogy with BEP-OSP, CEM was also extended by the concept of BEP to BEP-based constrained energy minimization (BEP-CEM) in Chang et al. (2000).
Phase (1) Band Generation Process
Phase (2) CEM
31.3.3 BEP-Based RX-Detector
Despite the fact that using BEP to develop BEP-OSP and BEP-CEM was investigated in Ren and Chang (2000a) and Chang et al. (2000), respectively, it is interesting to note that the concept of using BEP as BDE for RXD to derive a BEP-Based RX-detector (BEP-RXD) has never been explored. In what follows, we summarize its implementation.
Phase (1) Band Generation Process
Phase (2) RXD
One note on BEP-RXD is worth being mentioned. In addition to CEM and RXD, adaptive RXDs (ARXD) and adaptive CEM (ACEM), both of which using adaptive window sizes to form local covariance/covariance matrices to expand BEP to their corresponding generalized versions in exactly the same way as BEP-RXD is done, referred to as BEP-ARXD and BEP-ACEM. Figure 31.3 summarizes the utility of BDE in various operators and transformations where BEP-MLC is a BEP-based maximum likelihood classifier, which operates MLC on the BEP-expanded data space.
Figure 31.3 Band dimensionality expansion techniques for multispectral imagery.
