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Abstract:
In hyperspectral imagery one pixel typically consists of a
mixture of the reflectance spectra of several materials, where the
mixture coefficients correspond to the abundances of the
constituting materials. We assume linear combinations of
reflectance spectra with some additive normal sensor noise and
derive a probabilistic MAP framework for analyzing hyperspectral
data. As the material reflectance characteristics are not known a
priori, we face the problem of unsupervised linear positivity and
normalization of the abundances) naturally leads to a family of
interesting algorithms, for example in the noise-free case yielding
an algorithm that can be understood as constrained independent
component analysis (ICA). Simulations underline the usefulness of
our theory.
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