Hyperspectral imaging techniques have been developed for a wide range of remote sensing applications in both civilian and military, including terrain classification, environmental monitoring, agricultural monitoring, geological exploration, and military surveillance. A common problem in hyperspectral imaging is that a large part of pixels contain more than one type of spectral signatures (or endmembers). The hyperspectal unmixing problem aims at identifying the hidden endmembers and their corresponding proportions (or abundances) from an observed hyperspectral scene. In planetary exploration, hyperspectral unmixing provides a powerful tool for analyzing the composition and mineralogy of the observed planetary surfaces. In this thesis, we propose a hyperspectral unmixing algorithm using convex analysis. The algorithm, called the minimum simplex volume algorithm (MSVA), considers a challenging case where no pure pixel is assumed to be present. It is an alternating minimization approach for hyperspectral image unmixing using a minimum simplex volume criterion. We provide a hyperspectral unmixing formulation where the goal is to find a ‘best’ data-enclosing simplex by minimizing the simplex volume. We then propose a novel cyclic minimization procedure that uses linear programs (LPs) to sequentially reduce the simplex volume. The MVSA is based on solving LPs, and hence it can be efficiently implemented by using readily available LP solvers. And the proposed algorithm is capable of obtaining endmembers and fractional abundances simultaneously. Some Monde Carlo simulations and real data experiments are presented to demonstrate the efficacy of the proposed method over several existing unmixing methods.

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