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Stochastic and Deterministic Tensorization for Blind Signal Separation

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Latent Variable Analysis and Signal Separation (LVA/ICA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9237))

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Abstract

Given an instantaneous mixture of some source signals, the blind signal separation (BSS) problem consists of the identification of both the mixing matrix and the original sources. By itself, it is a non-unique matrix factorization problem, while unique solutions can be obtained by imposing additional assumptions such as statistical independence. By mapping the matrix data to a tensor and by using tensor decompositions afterwards, uniqueness is ensured under certain conditions. Tensor decompositions have been studied thoroughly in literature. We discuss the matrix to tensor step and present tensorization as an important concept on itself, illustrated by a number of stochastic and deterministic tensorization techniques.

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Notes

  1. 1.

    Note that the autocorrelation is not required for each source for each of the lags.

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Acknowledgements

The research is funded by (1) a Ph.D. grant of the Agency for Innovation by Science and Technology (IWT), (2) Research Council KU Leuven: CoE PFV/10/002 (OPTEC), (3) F.W.O.: projects G.0830.14N and G.0881.14N, (4) the Belgian Federal Science Policy Office: IUAP P7/19 (DYSCO II, Dynamical systems, control and optimization, 2012–2017), (5) EU: The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013) / ERC Advanced Grant: BIOTENSORS (no. 339804). This paper reflects only the authors’ views and the Union is not liable for any use that may be made of the contained information.

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Authors and Affiliations

  1. Department of Electrical Engineering (ESAT) – STADIUS Center for Dynamical Systems, Signal Processing and Data Analytics, KU Leuven, Kasteelpark Arenberg 10, 3001, Leuven, Belgium

    Otto Debals & Lieven De Lathauwer

  2. Group Science, Engineering and Technology, KU Leuven Kulak, E. Sabbelaan 53, 8500, Kortrijk, Belgium

    Otto Debals & Lieven De Lathauwer

  3. iMinds Medical IT, KU Leuven, Kasteelpark Arenberg 10, 3001, Leuven, Belgium

    Otto Debals & Lieven De Lathauwer

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  1. Otto Debals
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  2. Lieven De Lathauwer
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Correspondence to Otto Debals .

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Editors and Affiliations

  1. Inria, Villers-les-Nancy, France

    Emmanuel Vincent

  2. Tel Aviv University, Tel-Aviv, Israel

    Arie Yeredor

  3. Technical University of Libere, Liberec, Czech Republic

    Zbyněk Koldovský

  4. The Czech Academy of Sciences, Prague, Czech Republic

    Petr Tichavský

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Debals, O., De Lathauwer, L. (2015). Stochastic and Deterministic Tensorization for Blind Signal Separation. In: Vincent, E., Yeredor, A., Koldovský, Z., Tichavský, P. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2015. Lecture Notes in Computer Science(), vol 9237. Springer, Cham. https://doi.org/10.1007/978-3-319-22482-4_1

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  • DOI: https://doi.org/10.1007/978-3-319-22482-4_1

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