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Source Separation in the Presence of Side Information: Necessary and Sufficient Conditions for Reliable De-Mixing

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

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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.

Type: Proceedings paper
Title: Source Separation in the Presence of Side Information: Necessary and Sufficient Conditions for Reliable De-Mixing
Event: IEEE Global Conference on Signal and Information Processing (GlobalSIP)
Location: Anaheim (CA), USA
Dates: 26th-29th November 2018
ISBN-13: 978-1-7281-1295-4
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/GlobalSIP.2018.8646499
Publisher version: https://doi.org/10.1109/GlobalSIP.2018.8646499
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Source separation, Reliability theory, Atmospheric measurements, Particle measurements, Pollution measurement, Covariance matrices
UCL classification: UCL
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UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Electronic and Electrical Eng
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10073199
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