Hyperspectral Data Processing: Algorithm Design and Analysis

31.2 Band Dimensionality Expansion

As shown in Chang and Brumbley (1999a, 1999b), the performance of OSP was considerably degraded if it was used for multispectral image classification due to an insufficient number of spectral bands to be used for orthogonal subspace projection. In order to address this issue, a recent effort in extending OSP to multispectral imagery was investigated by Ren and Chang (2000a) where an extended version of OSP, called Generalized OSP (GOSP), was developed by including a new technique, referred to as BGP, which allows users to expand spectral band dimensionality via nonlinear functions.

31.2.1 Rationale for Developing BDE

The idea of the BGP developed in Ren and Chang (2000a) arises from a second-order random process specified by the first-order and second-order statistics. If we view the original spectral bands image as the first-order statistical images, we can generate a set of second-order statistical spectral bands that capture correlation between spectral bands. These correlated images provide useful second-order statistical information among bands, which is missing in the set of the original spectral bands. The desired second-order statistics including auto-correlation, cross-correlation, and nonlinear correlation can be used to create nonlinearly correlated images. If there is a need of statistics of high orders, the same process can be carried out for this purpose. The concept of producing second-order or high-order correlated spectral bands ...