  Spectral variability is one of the major issue when conducting hyperspectral
unmixing. Within a given image composed of some elementary materials (herein
referred to as endmember classes), the spectral signature characterizing these
classes may spatially vary due to intrinsic component fluctuations or external
factors (illumination). These redundant multiple endmember spectra within each
class adversely affect the performance of unmixing methods. This paper proposes
a mixing model that explicitly incorporates a hierarchical structure of
redundant multiple spectra representing each class. The proposed method is
designed to promote sparsity on the selection of both spectra and classes
within each pixel. The resulting unmixing algorithm is able to adaptively
recover several bundles of endmember spectra associated with each class and
robustly estimate abundances. In addition, its flexibility allows a variable
number of classes to be present within each pixel of the hyperspectral image to
be unmixed. The proposed method is compared with other state-of-the-art
unmixing methods that incorporate sparsity using both simulated and real
hyperspectral data. The results show that the proposed method can successfully
determine the variable number of classes present within each class and estimate
the corresponding class abundances.
