Multitemporal hyperspectral unmixing (MTHU) is a fundamental tool in the
analysis of hyperspectral image sequences. It reveals the dynamical evolution
of the materials (endmembers) and of their proportions (abundances) in a given
scene. However, adequately accounting for the spatial and temporal variability
of the endmembers in MTHU is challenging, and has not been fully addressed so
far in unsupervised frameworks. In this work, we propose an unsupervised MTHU
algorithm based on variational recurrent neural networks. First, a stochastic
model is proposed to represent both the dynamical evolution of the endmembers
and their abundances, as well as the mixing process. Moreover, a new model
based on a low-dimensional parametrization is used to represent spatial and
temporal endmember variability, significantly reducing the amount of variables
to be estimated. We propose to formulate MTHU as a Bayesian inference problem.
However, the solution to this problem does not have an analytical solution due
to the nonlinearity and non-Gaussianity of the model. Thus, we propose a
solution based on deep variational inference, in which the posterior
distribution of the estimated abundances and endmembers is represented by using
a combination of recurrent neural networks and a physically motivated model.
The parameters of the model are learned using stochastic backpropagation.
Experimental results show that the proposed method outperforms state of the art
MTHU algorithms