Hyperspectral Remote Sensing Image Endmember Extraction Algorithm Based on Minimum Simplex Volume Criterion

In this document, we discuss the algorithm implementation for extracting endmembers from hyperspectral remote sensing images. The core principle utilizes the minimum simplex volume criterion, where the algorithm computationally identifies the smallest geometric simplex (a generalized tetrahedron in n-dimensional space) that encloses all spectral data points. The implementation typically involves: - Preprocessing the hyperspectral data cube to reduce dimensionality using techniques like PCA or MNF - Solving an optimization problem to minimize the simplex volume containing all pixel spectra - Identifying simplex vertices as endmembers representing pure material signatures Key algorithmic steps include: 1. Initial endmember selection via pixel purity index or other initialization methods 2. Iterative volume minimization using convex geometry computations 3. Convergence verification when simplex volume reaches local minimum By extracting these fundamental endmembers, we achieve precise characterization of material spectral properties within the scene. This enables diverse applications including mineral mapping, vegetation analysis, and environmental monitoring. The algorithm has demonstrated computational efficiency and accuracy across multiple hyperspectral datasets, with robust performance in handling mixed pixels and spectral variability.