Hyperspectral Data Processing: Algorithm Design and Analysis

13

Fisher's Linear Spectral Mixture Analysis

A commonly used criterion to design techniques for linear spectral mixture analysis (LSMA) is least squares error (LSE) and referred to as least squares (LS)-LSMA. It is also shown in Chapter 12 that the functional form of a matched filter carried out by unconstrained LS-LSMA is essentially identical to that operated by the orthogonal subspace projection (OSP) approach using signal-to-noise ratio (SNR) as a criterion. Unfortunately, it is also known that both criteria are not necessarily optimal for pattern classification. This chapter presents a new and alternative approach to LSMA, called Fisher's LSMA (FLSMA). It extends the well-known pure-pixel-based (i.e., hard decision-based) Fisher's linear discriminant analysis (FLDA) to perform LSMA. Interestingly, what can be derived for LSMA can also be developed for FLSMA. In particular, two types of constrained approaches to LSMA, target signature-constrained mixed pixel classification (TSCMPC) and target abundance-constrained mixed pixel classification (TACMPC) derived in Chang (2002b) and Chang (2003a), can also be developed in parallel for FLSMA, to be called feature vector constrained FLSMA (FVC-FLSMA) and abundance-constrained FLSMA (AC-FLSMA), respectively. Since Fisher's ratio used by FLSMA is a more appropriate criterion than LSE and SNR in classification, both FVC-FLSMA and AC-FLSMA can improve LS-LSMA and SNR-based OSP in mixed pixel classification and abundance fraction quantification. ...