Advances in Hyperspectral Image Processing Techniques

14Analytical Fully Constrained Least Squares Linear Spectral Mixture Analysis

Chein-I Chang¹ and Hsiao-Chi Li²

¹Remote Sensing Signal and Image Processing Laboratory, Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County, Baltimore, MD, USA

²Department of Electrical Engineering, National Taipei University of Technology, Taipei, Taiwan, Republic of China

14.1 Introduction

Linear spectral mixture analysis (LSMA) is one of the earliest applications in hyperspectral imaging. It has found its great potential and promise in many applications [1], specifically in linear spectral unmixing (LSU), which assumes that a data sample vector can be linearly mixed by a set of so‐called endmembers via a linear mixing model and then unmixes the data sample vectors in terms of abundance fractions of these endmembers. More specifically, assume that L is the number of spectral bands and r is an L‐dimensional image pixel vector. Let m₁, m₂, …, m_p denote p endmembers. A linear mixing model of r is given by

(14.1)

where M is an L × p endmember matrix, denoted by M = [m₁m₂ ⋯m_p], α = (α₁, α₂, …, α_p)^T is a p × 1 abundance column vector with α_j being the abundance fraction of the jth endmember m_j, and n is noise or can be interpreted as a measurement or model error.

Two challenging issues in making LSMA effective need to be solved. One is endmember finding ...