A robust alternating volume maximization algorithm for endmember extraction in hyperspectral images

Accurate estimation of endmember signatures and the associated abundances of a scene from its hyperspectral observations is at present, a challenging research area. Many of the existing hyper-spectral unmixing algorithms are based on Winter´s belief, which states that the vertices of the maximum volume simplex inside the data cloud (observations) will yield high fidelity estimates of the endmember signatures if pure-pixels exist. Based on Winter´s belief, we recently proposed a convex analysis based alternating volume maximization (AVMAX) algorithm. In this paper we develop a robust version of the AVMAX algorithm. Here, the presence of noise in the hyperspectral observations is taken into consideration with the original deterministic constraints suitably reformulated as probabilistic constraints. The subproblems involved are convex problems and they can be effectively solved using available convex optimization solvers. Monte Carlo simulations are presented to demonstrate the efficacy of the proposed RAVMAX algorithm over several existing pure-pixel based hyperspectral unmixing methods, including its predecessor, the AVMAX algorithm.