Hyperspectral Data Processing: Algorithm Design and Analysis

14.1 Introduction

LSMA has shown success in solving a variety of problems, such as subpixel detection, mixed pixel classification, quantification, etc. It assumes that there are p image endmembers, , and any image pixel vector r is a linear mixture of these p endmembers with appropriate abundance fractions, , with α_j corresponding to the abundance fraction of the jth endmember m_j as follows:

(12.1)

where n is interpreted as a model or measurement error and is the endmember matrix formed by . Because of mathematical tractability, LSMA is widely implemented without imposing any constraint on the abundance fractions of the image endmembers . However, it has been shown in the literature, for example, Chang (2003a), that AC-LSMA can improve abundance-unconstrained LSMA in many aspects, such as ...