  Hyperspectral unmixing is aimed at identifying the reference spectral
signatures composing an hyperspectral image and their relative abundance
fractions in each pixel. In practice, the identified signatures may vary
spectrally from an image to another due to varying acquisition conditions, thus
inducing possibly significant estimation errors. Against this background,
hyperspectral unmixing of several images acquired over the same area is of
considerable interest. Indeed, such an analysis enables the endmembers of the
scene to be tracked and the corresponding endmember variability to be
characterized. Sequential endmember estimation from a set of hyperspectral
images is expected to provide improved performance when compared to methods
analyzing the images independently. However, the significant size of
hyperspectral data precludes the use of batch procedures to jointly estimate
the mixture parameters of a sequence of hyperspectral images. Provided that
each elementary component is present in at least one image of the sequence, we
propose to perform an online hyperspectral unmixing accounting for temporal
endmember variability. The online hyperspectral unmixing is formulated as a
two-stage stochastic program, which can be solved using a stochastic
approximation. The performance of the proposed method is evaluated on synthetic
and real data. A comparison with independent unmixing algorithms finally
illustrates the interest of the proposed strategy.
