  This paper introduces a new sparse unmixing technique using archetypal
analysis (SUnAA). First, we design a new model based on archetypal analysis. We
assume that the endmembers of interest are a convex combination of endmembers
provided by a spectral library and that the number of endmembers of interest is
known. Then, we propose a minimization problem. Unlike most conventional sparse
unmixing methods, here the minimization problem is non-convex. We minimize the
optimization objective iteratively using an active set algorithm. Our method is
robust to the initialization and only requires the number of endmembers of
interest. SUnAA is evaluated using two simulated datasets for which results
confirm its better performance over other conventional and advanced techniques
in terms of signal-to-reconstruction error. SUnAA is also applied to Cuprite
dataset and the results are compared visually with the available geological map
provided for this dataset. The qualitative assessment demonstrates the
successful estimation of the minerals abundances and significantly improves the
detection of dominant minerals compared to the conventional regression-based
sparse unmixing methods. The Python implementation of SUnAA can be found at:
https://github.com/BehnoodRasti/SUnAA.
