Recursive Hyperspectral Band Processing of Growing Simplex Volume Analysis

Abstract

Recursive hyperspecrral band processing (RHBP) has shown promise in a variety of applications. For example, it provides progressive hyperspectral target detection maps (Chaps. 13–15) or progressive unmixed abundance fraction maps (Chaps. 16 and 17), so that these progressive band-varying profiles can be used to monitor their interband changes to identify band significance for image analysts. Interestingly, RHBP can also offer another major benefit for simplex volume (SV)-based endmember finding algorithms such as N-FINDR developed by Winter (1999a, b) and simplex growing algorithm (SGA) developed by Chang et al. (2006b). Since the number of endmembers, p, is relatively small compared to the number of total bands, L, used for data acquisition, it is a general practice for these algorithms to apply dimensionality reduction (DR) to reduce dimensionality from L to p−1 so that SV can be appropriately calculated by a matrix determinant of full rank. However, as shown in Chap. 2, SVs found from DR-data are not necessary true SVs. To resolve this issue, Chaps. 11 and 12 developed two different approaches to finding endmembers by calculating geometric SVs (GSVs) without DR. This chapter takes advantage of the techniques in Chaps. 11 and 12 to derive a third approach, called RHBP of growing simplex volume analysis (RHBP-GSVA), which extends SGA and orthogonal projection-based SGA (OPSGA) in Chap. 11 and geometric SGA (GSGA) in Chap. 12 to finding endmembers band by band progressively and recursively. Several benefits can be gained from RHBP-GSVA. First and foremost is that RHBP-GSVA allows users to find endmembers through progressive band-varying spectral profiles. Another is that it enables users to specify those bands that are significant to find different endmembers. Finally and most importantly, RHBP-GSVA provides a means of understanding the spectral characteristics of endmembers during the course of the endmember finding process.