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.
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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 UCL > Provost and Vice Provost Offices 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 UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of the Built Environment UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of the Built Environment > Bartlett School Env, Energy and Resources |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10073199 |
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