Blind Source Separation of Single Channel Mixture Using Tensorization and Tensor Diagonalization

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10169)


This paper deals with estimation of structured signals such as damped sinusoids, exponentials, polynomials, and their products from single channel data. It is shown that building tensors from this kind of data results in tensors with hidden block structure which can be recovered through the tensor diagonalization. The tensor diagonalization means multiplying tensors by several matrices along its modes so that the outcome is approximately diagonal or block-diagonal of 3-rd order tensors. The proposed method can be applied to estimation of parameters of multiple damped sinusoids, and their products with polynomial.


Blind source separation Block tensor decomposition Tensor diagonalization Three-way folding Three-way toeplitzation Damped sinusoids 


  1. 1.
    Cichocki, A., Zdunek, R., Phan, A.-H., Amari, S.: Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation. Wiley, Chichester (2009)CrossRefGoogle Scholar
  2. 2.
    Cichocki, A., Mandic, D., Caiafa, C., Phan, A.-H., Zhou, G., Zhao, Q., Lathauwer, L.D.: Multiway component analysis: tensor decompositions for signal processing applications. IEEE Sig. Process. Mag. 32(2), 145–163 (2015)CrossRefGoogle Scholar
  3. 3.
    Comon, P., Jutten, C. (eds.): Handbook of Blind Source Separation: Independent Component Analysis and Applications. Academic Press, Cambridge (2010)Google Scholar
  4. 4.
    Proakis, J., Manolakis, D.: Digital Signal Processing: Principles, Algorithms, Applications. Macmillan, London (1992)Google Scholar
  5. 5.
    Kumaresan, R., Tufts, D.: Estimating the parameters of exponentially damped sinusoids and pole-zero modelling in noise. IEEE Trans. Acoust. Speech Sig. Proces. 30(7), 837–840 (1982)Google Scholar
  6. 6.
    Hua, Y., Sarkar, T.: Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoid in noise. IEEE Trans. Acoust. Speech Sig. Process. 38(5), 814–824 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Papy, J.M., De Lathauwer, L., Van Huffel, S.: Exponential data fitting using multilinear algebra: the single-channel and the multichannel case. Numer. Linear Algebra Appl. 12(9), 809–826 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Nion, D., Sidiropoulos, N.D.: Tensor algebra and multidimensional harmonic retrieval in signal processing for MIMO radar. IEEE Trans. Sig. Process. 58, 5693–5705 (2010)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Wen, F., So, H.C.: Robust multi-dimensional harmonic retrieval using iteratively reweighted HOSVD. IEEE Sig. Process. Lett. 22, 2464–2468 (2015)CrossRefGoogle Scholar
  10. 10.
    Sørensen, M., De Lathauwer, L.: Multidimensional harmonic retrieval via coupled canonical polyadic decomposition - Part 1: model and identifiability. IEEE Trans. Sig. Process. 65(2), 517–527 (2017)MathSciNetCrossRefGoogle Scholar
  11. 11.
    De Lathauwer, L.: Blind separation of exponential polynomials and the decomposition of a tensor in rank-(\(L_r\),\(L_r\),1) terms. SIAM J. Matrix Anal. Appl. 32(4), 1451–1474 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    De Lathauwer, L.: Block component analysis, a new concept for blind source separation. In: Proceedings of the 10th International Conference on LVA/ICA, Tel Aviv, 12–15 March, pp. 1–8 (2012)Google Scholar
  13. 13.
    Tichavský, P., Phan, A.-H., Cichocki, A.: Tensor diagonalization-a new tool for PARAFAC and block-term decomposition (2014). arXiv preprint arXiv:1402.1673
  14. 14.
    Kouchaki, S., Sanei, S.: Tensor based singular spectrum analysis for nonstationary source separation. In: Proceedings of the 2013 IEEE International Workshop on Machine Learning for Signal Processing, Southampton, UK (2013)Google Scholar
  15. 15.
    Debals, O., Lathauwer, L.: Stochastic and deterministic tensorization for blind signal separation. In: Vincent, E., Yeredor, A., Koldovský, Z., Tichavský, P. (eds.) LVA/ICA 2015. LNCS, vol. 9237, pp. 3–13. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-22482-4_1 Google Scholar
  16. 16.
    Boussé, M., Debals, O., De Lathauwer, L.: A tensor-based method for large-scale blind source separation using segmentation. IEEE Trans. Sig. Process. 65(2), 346–358 (2017)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Cichocki, A., Namgil, L., Oseledets, I., Phan, A.-H., Zhao, Q., Mandic, D.P.: Tensor networks for dimensionality reduction and large-scale optimization. Found. Trends\(\textregistered \) Mach. Learn. 9(4–5) (2017)Google Scholar
  18. 18.
    Sorber, L., Van Barel, M., De Lathauwer, L.: Structured data fusion. IEEE J. Sel. Top. Sign. Proces. 9(4), 586–600 (2015)CrossRefGoogle Scholar
  19. 19.
    Hayes, M.: Statistical Digital Signal Processing and Modeling. Wiley, Hoboken (1996)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Lab for Advanced Brain Signal ProcessingBrain Science Institute - RIKENWakoJapan
  2. 2.Institute of Information Theory and AutomationPragueCzech Republic
  3. 3.Skolkovo Institute of Science and Technology (SKOLTECH)MoscowRussia

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