  Spectral unmixing methods incorporating spatial regularizations have
demonstrated increasing interest. Although spatial regularizers which promote
smoothness of the abundance maps have been widely used, they may overly smooth
these maps and, in particular, may not preserve edges present in the
hyperspectral image. Existing unmixing methods usually ignore these edge
structures or use edge information derived from the hyperspectral image itself.
However, this information may be affected by large amounts of noise or
variations in illumination, leading to erroneous spatial information
incorporated into the unmixing procedure. This paper proposes a simple, yet
powerful, spectral unmixing framework which incorporates external data (i.e.
LiDAR data). The LiDAR measurements can be easily exploited to adjust standard
spatial regularizations applied to the unmixing process. The proposed framework
is rigorously evaluated using two simulated datasets and a real hyperspectral
image. It is compared with competing methods that rely on spatial information
derived from a hyperspectral image. The results show that the proposed
framework can provide better abundance estimates and, more specifically, can
significantly improve the abundance estimates for pixels affected by shadows.
