  This paper presents three hyperspectral mixture models jointly with Bayesian
algorithms for supervised hyperspectral unmixing. Based on the residual
component analysis model, the proposed general formulation assumes the linear
model to be corrupted by an additive term whose expression can be adapted to
account for nonlinearities (NL), endmember variability (EV), or mismodelling
effects (ME). The NL effect is introduced by considering a polynomial
expression that is related to bilinear models. The proposed new formulation of
EV accounts for shape and scale endmember changes while enforcing a smooth
spectral/spatial variation. The ME formulation takes into account the effect of
outliers and copes with some types of EV and NL. The known constraints on the
parameter of each observation model are modeled via suitable priors. The
posterior distribution associated with each Bayesian model is optimized using a
coordinate descent algorithm which allows the computation of the maximum a
posteriori estimator of the unknown model parameters. The proposed mixture and
Bayesian models and their estimation algorithms are validated on both synthetic
and real images showing competitive results regarding the quality of the
inferences and the computational complexity when compared to the
state-of-the-art algorithms.
