7

Simultaneous Endmember Extraction Algorithms (SM-EEAs)

Endmembers provide fundamental understanding of hyperspectral data where an endmember is defined as an idealized pure signature used to specify a particular spectral class. With the advent of recently developed hyperspectral imaging sensors, which utilize hundreds of contiguous spectral channels with significantly improved spatial and spectral resolutions, it is now possible to find endmembers, an important and crucial task in hyperspectral data exploitation. On many occasions endmembers appear as anomalies, rare substances, small unidentified targets, which cannot be resolved by multispectral imaging sensors but in fact provide vital information. Over the past few years, many endmember extraction algorithms (EEAs) have been developed and reported in the public domain. One of the early developments in endmember extraction is pixel purity index (PPI) developed by Boardman (1994). Since then it has emerged as one of the most widely used EEAs due to its availability in the environment for visualizing images (ENVI) commercialized by the analytical imaging and geophysics (AIG) (Research Systems Inc., 2001). In addition to PPI, many other EEAs have also been developed, for example, minimum-volume transform (MVT) (Craig, 1994), convex cone analysis (CCA) (Ifarraguerri and Chang, 1999), N-finder algorithm (N-FINDR) (Winter, 1999), automated morphological endmember extraction (AMEE) algorithm (Plaza et al., 2002), iterative error analysis (IEA) developed by Neville et al. (1999), iterated constrained endmember (ICE) (Berman et al., 2004), vertex component analysis (VCA) (Nascimento and Dias, 2005), independent component analysis-based EEA (ICA-EEA) (Wang and Chang, 2006), simplex growing algorithm (SGA) (Chang et al., 2006), and so on. Technically speaking, an EEA must extract all the desired endmembers simultaneously, referred to as simultaneous EEA (SM-EEA) in this book. However, practically speaking, finding all endmembers simultaneously is generally associated with high computational cost because it involves a brute-force search among all data sample vectors. This is particularly severe for hyperspectral data with enormous volumes. Therefore, it is highly desirable if an EEA can be carried out to find endmembers sequentially, while also producing endmembers as close as those produced by an SM-EEA in the sense of spectral similarity. An EEA implemented in such a fashion is referred to as sequential EEA (SQ-EEA) in this book. According to this categorization, PPI, N-FINDR, MVT, CCA, and AMEE are considered as SM-EEAs as opposed to VCA, ICA-EEA, and SGA, which are actually SQ-EEAs. These two types of EEAs will be discussed in detail in two separate chapters: SM-EEA in this chapter followed by SQ-EEAs in Chapter 8. As will be seen in Chapter 8, SQ-EEAs are generally derived from their SM-EEA counterparts to ease computational complexity.