Hyperspectral Data Processing: Algorithm Design and Analysis

7.3 Second-Order Statistics-Based Endmember Extraction

Based on the nature of pure signatures using the concept of convexity geometry as a criterion to find endmembers seems natural and logical, but may not be the only way to accomplish the task of endmember extraction. Instead of appealing for geometric features such as convex hull, convex cone, and simplex described above, a rather different approach that uses the statistical spectral profile of a signature as a base to determine an endmember is of interest. More specifically, a set of spectrally distinct endmembers should constitute the least statistical spectral correlation among all possible data sets with the same number of data samples. In other words, if there is a data sample that is a mixture of other data samples in the same set, the statistical spectral correlation among members in this set should be greater than that of a set with the same number of data samples that are all endmembers. In this section, we explore such statistics-based approaches to endmember extraction. In particular, we are interested in second-order statistics with two criteria, statistical sample spectral correlation and LSE that can be used to design EEAs.

The second-order statistical sample correlation was previously explored by Singh and Harison (1985) who expressed the second-order statistics information in terms of correlation coefficients. Their idea was used by Eklundh and Singh (1993) to develop the so-called standardized principal components ...