Hyperspectral Data Processing: Algorithm Design and Analysis

15.1 Introduction

Linear mixture analysis is a theory developed for solving linear problems. It has found many successes in a wide range of applications, such as linear regression analysis in multivariate data analysis, blind source separation in signal processing, and partial volume estimation in magnetic resonance imaging (see Chapter 32). Specifically, LSMA has been widely used in remote sensing community to perform spectral unmixing (Chapters 12–14) where a data sample vector is linearly mixed by a number of so-called endmembers as a linear mixture from which it can be further unmixed as abundance fractions in terms of these endmembers. Using the same notations in Section 12.2 and Eq. (12.2) let r be an L-dimensional data sample vector and be signatures of interest that are used to unmix the sample vector r. To carry out spectral unmixing, a linear mixing model is required to represent r in terms of the following form:

(15.1)

where is a signature matrix, n is a noise vector and can be used to describe a model or measurement error, and is an unknown p-dimensional abundance vector ...