  Hyperspectral unmixing is a blind source separation problem which consists in
estimating the reference spectral signatures contained in a hyperspectral
image, as well as their relative contribution to each pixel according to a
given mixture model. In practice, the process is further complexified by the
inherent spectral variability of the observed scene and the possible presence
of outliers. More specifically, multi-temporal hyperspectral images, i.e.,
sequences of hyperspectral images acquired over the same area at different time
instants, are likely to simultaneously exhibit moderate endmember variability
and abrupt spectral changes either due to outliers or to significant time
intervals between consecutive acquisitions. Unless properly accounted for,
these two perturbations can significantly affect the unmixing process. In this
context, we propose a new unmixing model for multitemporal hyperspectral images
accounting for smooth temporal variations, construed as spectral variability,
and abrupt spectral changes interpreted as outliers. The proposed hierarchical
Bayesian model is inferred using a Markov chain Monte-Carlo (MCMC) method
allowing the posterior of interest to be sampled and Bayesian estimators to be
approximated. A comparison with unmixing techniques from the literature on
synthetic and real data allows the interest of the proposed approach to be
appreciated.
