A robust minimum volume enclosing simplex algorithm for hyperspectral unmixing

Hyperspectral unmixing is a process of extracting hidden spectral signatures (or endmembers) and the corresponding proportions (or abundances) of a scene, from its hyperspectral observations. Motivated by Craig's belief, we recently proposed an alternating linear programming based hyperspectral unmixing algorithm called minimum volume enclosing simplex (MVES) algorithm, which can yield good unmixing performance even for instances of highly mixed data. In this paper, we propose a robust MVES algorithm called RMVES algorithm, which involves probabilistic reformulation of the MVES algorithm, so as to account for the presence of noise in the observations. The problem formulation for RMVES algorithm is manifested as a chance constrained program, which can be suitably implemented using sequential quadratic programming (SQP) solvers in an alternating fashion. Monte Carlo simulations are presented to demonstrate the efficacy of the proposed RMVES algorithm over several existing benchmark hyperspectral unmixing methods, including the original MVES algorithm.