  Endmember (EM) variability has an important impact on the performance of
hyperspectral image (HI) analysis algorithms. Recently, extended linear mixing
models have been proposed to account for EM variability in the spectral
unmixing (SU) problem. The direct use of these models has led to severely
ill-posed optimization problems. Different regularization strategies have been
considered to deal with this issue, but none so far has consistently exploited
the information provided by the existence of multiple pure pixels often present
in HIs. In this work, we propose to break the SU problem into a sequence of two
problems. First, we use pure pixel information to estimate an interpolated
tensor of scaling factors representing spectral variability. This is done by
considering the spectral variability to be a smooth function over the HI and
confining the energy of the scaling tensor to a low-rank structure. Afterwards,
we solve a matrix-factorization problem to estimate the fractional abundances
using the variability scaling factors estimated in the previous step, what
leads to a significantly more well-posed problem. Simulation swith synthetic
and real data attest the effectiveness of the proposed strategy.
