Hyperspectral Data Processing: Algorithm Design and Analysis

17.6 ULSMA Versus Endmember Extraction

Early attempts of performing ULSMA have been focused on simultaneous implementation of endmember selection and LSMA such as combining PCA to determine their purity of selected endmembers, using convex geometry of a simplex to fit data to select endmembers (Boardman, 1993, 1994; Boardman et al. 1995). In addition, some efforts such as multiple endmember spectral mixture analysis in (Roberts et al., 1998; Dennison and Roberts, 2003) and endmember bundles in (Bates et al., 2000) were also proposed to deal with spectral variations of endmembers to be selected. Most recently, the concept of virtual endmembers (VEs) was also introduced in a modified spectral mixture analysis (Tompkins et al., 1997) for endmember selection in such a way that the VEs are those minimizing root-mean-square-error subject to user-specified constraints. The VEs were further explored for endmember selection in an optical real-time adaptive spectral identification system (ORASIS) developed in Bowles and Gilles (2007). One major issue arising in these approaches is unavailability of prior knowledge about how many endmember needed to be selected in the first place. Consequently, they did not perform endmember extraction but rather endmember selection. Specifically, in their approaches endmember selection and linear spectral unmixing must be implemented simultaneously where a prescribed threshold or physical constraints should be imposed to determine when the entire process ...