  Blind source separation (BSS) algorithms are unsupervised methods, which are
the cornerstone of hyperspectral data analysis by allowing for physically
meaningful data decompositions. BSS problems being ill-posed, the resolution
requires efficient regularization schemes to better distinguish between the
sources and yield interpretable solutions. For that purpose, we investigate a
semi-supervised source separation approach in which we combine a projected
alternating least-square algorithm with a learning-based regularization scheme.
In this article, we focus on constraining the mixing matrix to belong to a
learned manifold by making use of generative models. Altogether, we show that
this allows for an innovative BSS algorithm, with improved accuracy, which
provides physically interpretable solutions. The proposed method, coined sGMCA,
is tested on realistic hyperspectral astrophysical data in challenging
scenarios involving strong noise, highly correlated spectra and unbalanced
sources. The results highlight the significant benefit of the learned prior to
reduce the leakages between the sources, which allows an overall better
disentanglement.
