Hyperspectral Data Processing: Algorithm Design and Analysis

15

Kernel-Based Linear Spectral Mixture Analysis

Linear spectral mixture analysis (LSMA) has been widely used in remote sensing community for spectral unmixing and has enjoyed great success in material detection, classification, and identification. Recently, it has been extended in various approaches to linear spectral random mixture analysis (Chapter 15, Chang 2003a), Fisher's LSMA (FLSMA) in Chapter 13 and weighted abundance-constrained LSMA (WAC-LSMA) in Chapter 14 so as to enhance its performance. All these extensions also inherit drawbacks and limitations of LSMA when it comes to solving linear nonseparable problems. This chapter develops a kernel-based LSMA (KLSMA) to resolve the issue of nonlinear separability. By mapping the original data to a feature space via a nonlinear kernel, LSMA extensions can be further expanded to their kernel-based counterparts, specifically, the three backbone least squares-based LSMA (LS-LSMA) techniques (Chang 2003a), least squares orthogonal subspace projection (LSOSP), non-negativity constrained least squares (NCLS), and fully constrained least squares (FCLS), are readily extended to their corresponding kernel versions, KLSOSP, KNCLS, and KFCLS. Interestingly, according to experiments conducted based on synthetic and real images, KLSMA can be more effective than LSMA only for cases where data sample vectors are heavily mixed, specifically for multispectral imagery which will be discussed in Chapters 31 and 32.