Hyperspectral unmixing based on mixtures of dirichlet components
IEEE Transactions on Geoscience and Remote Sensing, PP (99):
1--16 (2011)DOI: 10.1109/TGRS.2011.2163941
Abstract
This paper introduces a new unsupervised hyperspectral unmixing method
conceived to linear but highly mixed hyperspectral data sets, in
which the simplex of minimum volume, usually estimated by the purely
geometrically based algorithms, is far way from the true simplex
associated with the endmembers. The proposed method, an extension
of our previous studies, resorts to the statistical framework. The
abundance fraction prior is a mixture of Dirichlet densities, thus
automatically enforcing the constraints on the abundance fractions
imposed by the acquisition process, namely, nonnegativity and sum-to-one.
A cyclic minimization algorithm is developed where the following
are observed: 1) The number of Dirichlet modes is inferred based
on the minimum description length principle; 2) a generalized expectation
maximization algorithm is derived to infer the model parameters;
and 3) a sequence of augmented Lagrangian-based optimizations is
used to compute the signatures of the endmembers. Experiments on
simulated and real data are presented to show the effectiveness of
the proposed algorithm in unmixing problems beyond the reach of the
geometrically based state-of-the-art competitors.