  Hyperspectral images provide a rich representation of the underlying spectrum
for each pixel, allowing for a pixel-wise classification/segmentation into
different classes. As the acquisition of labeled training data is very
time-consuming, unsupervised methods become crucial in hyperspectral image
analysis. The spectral variability and noise in hyperspectral data make this
task very challenging and define special requirements for such methods.
  Here, we present a novel unsupervised hyperspectral segmentation framework.
It starts with a denoising and dimensionality reduction step by the
well-established Minimum Noise Fraction (MNF) transform. Then, the Mumford-Shah
(MS) segmentation functional is applied to segment the data. We equipped the MS
functional with a novel robust distribution-dependent indicator function
designed to handle the characteristic challenges of hyperspectral data. To
optimize our objective function with respect to the parameters for which no
closed form solution is available, we propose an efficient fixed point
iteration scheme. Numerical experiments on four public benchmark datasets show
that our method produces competitive results, which outperform three
state-of-the-art methods substantially on three of these datasets.
