III
Supervised Linear Hyperspectral Mixture Analysis
Linear spectral mixture analysis (LSMA) is a theory developed for linear spectral unmixing (LSU). It assumes that data sample vectors can be represented by linear mixtures of a finite number of basic component constituent spectra, known as endmembers. More specifically, let 
be p such basic component constituent spectra and r be the spectral signature of a data sample vector. The LSMA models r as 
with αj being the abundance fraction of mj resident in the data sample vector r where the term n is included to account for a model error or a noise factor. So, according to LSMA, there are two sets of parameters, 
and 
needed to be solved and LSU is developed as a technique to find 
associated with 
. As a consequence, in order to carry out LSU effectively, three-stage processes must be performed in sequence. The first-stage process is to estimate ...
