Hyperspectral Data Processing: Algorithm Design and Analysis

17.7 Conclusions

The performance of LSMA is completely determined by the number of signatures, p and signatures used to form a linear mixing model to unmix data sample vectors. Unfortunately, in real applications none of these two pieces of information is known accurately in advance. So, a key to success in LSMA is to find an appropriate signature matrix M to form a linear mixing model in (2.75) where r is an image pixel vector and n is a model correction term. In supervised LSMA (SLSMA), this matrix M is assumed to be known a priori. However, when it comes to ULSMA the knowledge of the signature matrix M is not available and must be obtained directly from the data. The two unsupervised approaches, LS-UVSFA in Section 17.2 and CA-UVSFA in Section 17.3, provide a means of finding such an unsupervised signature matrix M for ULSMA. Since the signatures found in the unsupervised signature matrix, M, are real data sample vectors and may not be pure as true endmembers assumed in SLSMA, they are called virtual signatures (VSs) for their distinction from true endmembers. So, the signature matrix M formed by VSs is also referred to as VS matrix. The performance of ULSMA is completely determined by two factors, the number of VSs, p, and the VSs used to form a linear mixing model, both of which ...