Hyperspectral Data Processing: Algorithm Design and Analysis

32.4 Kernel-Based Linear Spectral Mixture Analysis

The BEP presented in Section 32.2.2 is developed to resolve the issue of insufficient band dimensionality so that LSMA techniques such as OSP can still be effective by incorporating expanded images. This section presents a complete opposite approach, called kernel-based LSMA techniques developed in Chapter 15 for MR image analysis. Instead of expanding the original band dimensionality, we introduce nonlinear kernels into LSMA-based classifiers in Section 32.2.1 to make them perform linear decisions in a high dimensional feature space to solve linear non-separable problems in the original MR image data space by mapping the original MRI data space to a new feature space to deal with the issue of linear non-separable features. As a result, the four LSMA-based classifiers, OSP, LSOSP, NCLS and FCLS in Chapter 12 can be further extended to their kernel versions, Kernel Orthogonal Subspace Projection (K-OSP), Kernel LSOSP (K-LSOSP), Kernel Non-negative Constrained Least Squares (K-NCLS) and Kernel Fully Constrained Least Squares (K-FCLS) as discussed in Chapter 15 for hyperspectral imaging and in Section 31.4 of Chapter 31 for multispectral imaging. For details we refer readers to these two chapters. Since OSP and KOSP are originally developed for abundance detection not estimation, they are not of particular interest in PVE. Only three kernel versions of LSMA are studied for MR image experiments.