  Hyperspectral unmixing allows representing mixed pixels as a set of pure
materials weighted by their abundances. Spectral features alone are often
insufficient, so it is common to rely on other features of the scene. Matrix
models become insufficient when the hyperspectral image (HSI) is represented as
a high-order tensor with additional features in a multimodal, multifeature
framework. Tensor models such as canonical polyadic decomposition allow for
this kind of unmixing but lack a general framework and interpretability of the
results. In this article, we propose an interpretable methodological framework
for low-rank multifeature hyperspectral unmixing based on tensor decomposition
(MultiHU-TD) that incorporates the abundance sum-to-one constraint in the
alternating optimization alternating direction method of multipliers (ADMM)
algorithm and provide in-depth mathematical, physical, and graphical
interpretation and connections with the extended linear mixing model. As
additional features, we propose to incorporate mathematical morphology and
reframe a previous work on neighborhood patches within MultiHU-TD. Experiments
on real HSIs showcase the interpretability of the model and the analysis of the
results. Python and MATLAB implementations are made available on GitHub.
