Index Terms-blind source separation, sparsity, metric learning, physical constraint ABSTRACT Sparse Blind source separation (sBSS) is an unsupervised matrix factorization problem, which is now a key tool to analyse multispectral data, especially in astrophysics. Being an ill-posed problem, designing priors is crucial. In the present paper, we investigate how the prior knowledge based on examples of physical spectra can be exploited in sBSS, based on the projection onto the barycentric span of these examples. For that purpose, we investigate different metrics to build such projections, and further introduce a novel machine learning approach to build physically relevant reconstruction. Secondly, we show how this can be deployed to design a semi-blind sparse BSS method coined. Preliminary numerical results on realistic astrophysical X-ray images show very promising separation results.