  Hyperspectral unmixing is one of the crucial steps for many hyperspectral
applications. The problem of hyperspectral unmixing has proven to be a
difficult task in unsupervised work settings where the endmembers and
abundances are both unknown. What is more, this task becomes more challenging
in the case that the spectral bands are degraded with noise. This paper
presents a robust model for unsupervised hyperspectral unmixing. Specifically,
our model is developed with the correntropy based metric where the non-negative
constraints on both endmembers and abundances are imposed to keep physical
significance. In addition, a sparsity prior is explicitly formulated to
constrain the distribution of the abundances of each endmember. To solve our
model, a half-quadratic optimization technique is developed to convert the
original complex optimization problem into an iteratively re-weighted NMF with
sparsity constraints. As a result, the optimization of our model can adaptively
assign small weights to noisy bands and give more emphasis on noise-free bands.
In addition, with sparsity constraints, our model can naturally generate sparse
abundances. Experiments on synthetic and real data demonstrate the
effectiveness of our model in comparison to the related state-of-the-art
unmixing models.
