@inproceedings{discovery10073199,
           pages = {351--355},
       booktitle = {Proceedings of the 2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP)},
           title = {Source Separation in the Presence of Side Information: Necessary and Sufficient Conditions for Reliable De-Mixing},
       publisher = {IEEE},
            note = {This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.},
         journal = {2018 IEEE GLOBAL CONFERENCE ON SIGNAL AND INFORMATION PROCESSING (GLOBALSIP 2018)},
         address = {Danvers (MA), USA},
           month = {February},
            year = {2019},
            issn = {2376-4066},
        keywords = {Source separation, Reliability theory, Atmospheric measurements, Particle measurements, Pollution measurement, Covariance matrices},
          author = {Sabetsarvestani, Z and Renna, F and Kiraly, F and Rodrigues, MRD},
             url = {https://doi.org/10.1109/GlobalSIP.2018.8646499},
        abstract = {This paper puts forth new recovery guarantees for the source separation problem in the presence of side information, where one observes the linear superposition of two source signals plus two additional signals that are correlated with the mixed ones. By positing that the individual components of the mixed signals as well as the corresponding side information signals follow a joint Gaussian mixture model, we characterise necessary and sufficient conditions for reliable separation in the asymptotic regime of low-noise as a function of the geometry of the underlying signals and their interaction. In particular, we show that if the subspaces spanned by the innovation components of the source signals with respect to the side information signals have zero intersection, provided that we observe a certain number of measurements from the mixture, then we can reliably separate the sources, otherwise we cannot. We also provide a number of numerical results on synthetic data that validate our theoretical findings.}
}