In blind hyperspectral unmixing (HU), the pure-pixel assumption is well-knownto be powerful in enabling simple and effective blind HU solutions. However,the pure-pixel assumption is not always satisfied in an exact sense, especiallyfor scenarios where pixels are heavily mixed. In the no pure-pixel case, a goodblind HU approach to consider is the minimum volume enclosing simplex (MVES).Empirical experience has suggested that MVES algorithms can perform wellwithout pure pixels, although it was not totally clear why this is true from atheoretical viewpoint. This paper aims to address the latter issue. We developan analysis framework wherein the perfect endmember identifiability of MVES isstudied under the noiseless case. We prove that MVES is indeed robust againstlack of pure pixels, as long as the pixels do not get too heavily mixed and tooasymmetrically spread. The theoretical results are verified by numericalsimulations.
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