eprintid: 10073199 rev_number: 24 eprint_status: archive userid: 608 dir: disk0/10/07/31/99 datestamp: 2019-05-07 11:45:06 lastmod: 2021-03-07 00:55:11 status_changed: 2019-05-07 11:45:06 type: proceedings_section metadata_visibility: show creators_name: Sabetsarvestani, Z creators_name: Renna, F creators_name: Kiraly, F creators_name: Rodrigues, MRD title: Source Separation in the Presence of Side Information: Necessary and Sufficient Conditions for Reliable De-Mixing ispublished: pub divisions: UCL divisions: A01 divisions: B04 divisions: C05 divisions: F46 divisions: C06 divisions: F61 divisions: C04 divisions: F34 keywords: Source separation, Reliability theory, Atmospheric measurements, Particle measurements, Pollution measurement, Covariance matrices note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. 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. date: 2019-02-21 date_type: published publisher: IEEE official_url: https://doi.org/10.1109/GlobalSIP.2018.8646499 oa_status: green full_text_type: other language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 1649478 doi: 10.1109/GlobalSIP.2018.8646499 isbn_13: 978-1-7281-1295-4 language_elements: English lyricists_name: Kiraly, Franz lyricists_name: Rodrigues, Miguel lyricists_name: Sabetsarvestani, Zahra lyricists_id: FJKIR17 lyricists_id: MRDIA06 lyricists_id: ZSABE20 actors_name: Sabetsarvestani, Zahra actors_id: ZSABE20 actors_role: owner full_text_status: public publication: 2018 IEEE GLOBAL CONFERENCE ON SIGNAL AND INFORMATION PROCESSING (GLOBALSIP 2018) place_of_pub: Danvers (MA), USA pagerange: 351-355 pages: 5 event_title: IEEE Global Conference on Signal and Information Processing (GlobalSIP) event_location: Anaheim (CA), USA event_dates: 26th-29th November 2018 institution: IEEE Global Conference on Signal and Information Processing (GlobalSIP) issn: 2376-4066 book_title: Proceedings of the 2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP) citation: Sabetsarvestani, Z; Renna, F; Kiraly, F; Rodrigues, MRD; (2019) Source Separation in the Presence of Side Information: Necessary and Sufficient Conditions for Reliable De-Mixing. In: Proceedings of the 2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP). (pp. pp. 351-355). IEEE: Danvers (MA), USA. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10073199/7/Rodrigues_Source%20Separation%20in%20the%20Presence%20of%20Side%20Information.%20Necessary%20and%20Sufficient%20Conditions%20for%20Reliable%20De-Mixing_AAM.pdf