  Mixing phenomena in hyperspectral images depend on a variety of factors such
as the resolution of observation devices, the properties of materials, and how
these materials interact with incident light in the scene. Different parametric
and nonparametric models have been considered to address hyperspectral unmixing
problems. The simplest one is the linear mixing model. Nevertheless, it has
been recognized that mixing phenomena can also be nonlinear. The corresponding
nonlinear analysis techniques are necessarily more challenging and complex than
those employed for linear unmixing. Within this context, it makes sense to
detect the nonlinearly mixed pixels in an image prior to its analysis, and then
employ the simplest possible unmixing technique to analyze each pixel. In this
paper, we propose a technique for detecting nonlinearly mixed pixels. The
detection approach is based on the comparison of the reconstruction errors
using both a Gaussian process regression model and a linear regression model.
The two errors are combined into a detection statistics for which a probability
density function can be reasonably approximated. We also propose an iterative
endmember extraction algorithm to be employed in combination with the detection
algorithm. The proposed Detect-then-Unmix strategy, which consists of
extracting endmembers, detecting nonlinearly mixed pixels and unmixing, is
tested with synthetic and real images.
