Hyperspectral Data Processing: Algorithm Design and Analysis

8.6 High-Order Statistics-Based SQ-EEAS

In Section 7.3, a second-order statistics SM-EEA, SPCA-EEA, is derived to find a set of endmembers that yield the least statistical correlation. However, there are no HOS SM-EEAs that are similar to SPCA-EEA developed in Chapter 7. The reason for this is that no analytic form can be derived for HOS-EEAs in the same way as SPCA-EEA that solves a characteristic polynomial equation to find all eigenvalues simultaneously. In this case, instead of solving a known equation such as the characteristic polynomial equation, HOS-based EEAs must appeal for an algorithm that allows one to find projection vectors similar to eigenvectors found by SPCA-EEA through eigenvalues and each of such projection vectors can only be found one at a time. Then, each projection vector produces an HOS component from which an endmember can be extracted. An EEA design, based on this approach, is called an HOS-based SQ-EEA.

More specifically, we assume that the ith HOS component, denoted by , can be described by a random variable ζ_i with values taken by the gray level value of the nth pixel in the component , denoted by . Therefore, criteria used to generate various HOS components ...