  In blind hyperspectral unmixing (HU), the pure-pixel assumption is well-known
to be powerful in enabling simple and effective blind HU solutions. However,
the pure-pixel assumption is not always satisfied in an exact sense, especially
for scenarios where pixels are heavily mixed. In the no pure-pixel case, a good
blind HU approach to consider is the minimum volume enclosing simplex (MVES).
Empirical experience has suggested that MVES algorithms can perform well
without pure pixels, although it was not totally clear why this is true from a
theoretical viewpoint. This paper aims to address the latter issue. We develop
an analysis framework wherein the perfect endmember identifiability of MVES is
studied under the noiseless case. We prove that MVES is indeed robust against
lack of pure pixels, as long as the pixels do not get too heavily mixed and too
asymmetrically spread. The theoretical results are verified by numerical
simulations.
