  Endmember (EM) spectral variability can greatly impact the performance of
standard hyperspectral image analysis algorithms. Extended parametric models
have been successfully applied to account for the EM spectral variability.
However, these models still lack the compromise between flexibility and
low-dimensional representation that is necessary to properly explore the fact
that spectral variability is often confined to a low-dimensional manifold in
real scenes. In this paper we propose to learn a spectral variability model
directly form the observed data, instead of imposing it \emph{a priori}. This
is achieved through a deep generative EM model, which is estimated using a
variational autoencoder (VAE). The encoder and decoder that compose the
generative model are trained using pure pixel information extracted directly
from the observed image, what allows for an unsupervised formulation. The
proposed EM model is applied to the solution of a spectral unmixing problem,
which we cast as an alternating nonlinear least-squares problem that is solved
iteratively with respect to the abundances and to the low-dimensional
representations of the EMs in the latent space of the deep generative model.
Simulations using both synthetic and real data indicate that the proposed
strategy can outperform the competing state-of-the-art algorithms.
