  Given a mixed hyperspectral data set, linear unmixing aims at estimating the
reference spectral signatures composing the data - referred to as endmembers -
their abundance fractions and their number. In practice, the identified
endmembers can vary spectrally within a given image and can thus be construed
as variable instances of reference endmembers. Ignoring this variability
induces estimation errors that are propagated into the unmixing procedure. To
address this issue, endmember variability estimation consists of estimating the
reference spectral signatures from which the estimated endmembers have been
derived as well as their variability with respect to these references. This
paper introduces a new linear mixing model that explicitly accounts for spatial
and spectral endmember variabilities. The parameters of this model can be
estimated using an optimization algorithm based on the alternating direction
method of multipliers. The performance of the proposed unmixing method is
evaluated on synthetic and real data. A comparison with state-of-the-art
algorithms designed to model and estimate endmember variability allows the
interest of the proposed unmixing solution to be appreciated.
