Convex analysis based minimum-volume enclosing simplex algorithm for hyperspectral unmixing

Abstract—Hyperspectral unmixing aims at identifying the hidden spectral signatures (or endmembers) and their corresponding proportions (or abundances) from an observed hyperspectral scene. Many existing hyperspectral unmixing algorithms were developed under a commonly used assumption that pure pixels exist. However, the pure-pixel assumption may be seriously violated for highly mixed data. Based on intuitive grounds, Craig reported an unmixing criterion without requiring the pure-pixel assumption, which estimates the endmembers by vertices of a minimum-volume simplex enclosing all the observed pixels. In this paper, we incorporate convex analysis and Craig’s criterion to develop a minimum-volume enclosing simplex (MVES) formulation for hyperspectral unmixing. A cyclic minimization algorithm for approximating the MVES problem is developed using linear programs (LPs), which can be practically implemented by readily available LP solvers. We also provide a nonheuristic guarantee of our...

• Type: Conference
• Year: 2009
• Where: ICASSP
• Authors: Tsung-Han Chan, Chong-Yung Chi, Yu-Min Huang, Wing-Kin Ma
• Keywords: Abstract—Hyperspectral Unmixing Aims, Hyperspectral Unmixing Algorithms, ICASSP 2009, Pure Pixels, Signal Processing