Abstract
Hyperspectral unmixing is a process of extracting the spectral signatures (endmember signatures) and the corresponding fractions (abundance maps), which represent the proportional contribution of each endmember over the surface, from the given hyperspectral data. In this thesis, we focus on the study of how to accurately estimate the endmember signatures in the presence of noise in the observed data. A branch of existing hyperspectral unmixing algorithms is based on Winter's endmember extraction belief, which indicates that in the presence of pure pixels (the pixels are contributed by a single endmember only), the endmembers can be determined by finding the vertices of the maximum-volume simplex inside the data cloud. Nevertheless, in practice the endmember estimates yielded by Winter's belief are not in the proximity of true endmember signatures due to inevitable noise present in the data. Based on the robust Winter's belief and formulation \cite{Chan2011}, we propose two algorithms, namely worst-case robust alternating volume maximization (WCR-AVMAX) and worst-case robust successive volume maximization (WCR-SVMAX) which respectively apply alternating optimization and successive optimization to fulfill the robust Winter's belief. The former needs initialization while the later does not, and both are computationally efficient. Finally, we present computer simulations and real data experiments (AVIRIS hyperspectral data taken over the Cuprite mining site, Nevada, 1997 \cite{AVIRIS}) to demonstrate the superior performance and practical applicability of our proposed algorithms compared to several benchmark existing pure-pixel based algorithms.