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Circuits, Systems, and Signal Processing

, Volume 38, Issue 12, pp 5786–5816 | Cite as

Single-Channel Signal Separation Using Spectral Basis Correlation with Sparse Nonnegative Tensor Factorization

  • P. ParathaiEmail author
  • N. Tengtrairat
  • W. L. Woo
  • Bin Gao
Article

Abstract

A novel approach for solving the single-channel signal separation is presented the proposed sparse nonnegative tensor factorization under the framework of maximum a posteriori probability and adaptively fine-tuned using the hierarchical Bayesian approach with a new mixing mixture model. The mixing mixture is an analogy of a stereo signal concept given by one real and the other virtual microphones. An “imitated-stereo” mixture model is thus developed by weighting and time-shifting the original single-channel mixture. This leads to an artificial mixing system of dual channels which gives rise to a new form of spectral basis correlation diversity of the sources. Underlying all factorization algorithms is the principal difficulty in estimating the adequate number of latent components for each signal. This paper addresses these issues by developing a framework for pruning unnecessary components and incorporating a modified multivariate rectified Gaussian prior information into the spectral basis features. The parameters of the imitated-stereo model are estimated via the proposed sparse nonnegative tensor factorization with Itakura–Saito divergence. In addition, the separability conditions of the proposed mixture model are derived and demonstrated that the proposed method can separate real-time captured mixtures. Experimental testing on real audio sources has been conducted to verify the capability of the proposed method.

Keywords

Blind source separation Underdetermined mixture Tensor factorization Unsupervised learning Multiplicative updates Source modeling 

Notes

References

  1. 1.
    Y.I. Abramovich, O. Besson, A. Johnson, Conditional expected likelihood technique for compound-Gaussian and Gaussian distributed noise mixtures. Trans. Signal Process. 64, 6640–6649 (2016)MathSciNetzbMATHGoogle Scholar
  2. 2.
    A. Aissa-El-Bey, N. Linh-Trung, K. Abed-Meraim, A. Belouchrani, Y. Grenier, Under- determined blind separation of nondisjoint sources in the time-frequency domain. IEEE Trans. Signal Process. 55(3), 897–907 (2007)MathSciNetzbMATHGoogle Scholar
  3. 3.
    A. Al-Tmeme, W.L. Woo, S.S. Dlay, B. Gao, Underdetermined convolutive source separation using GEM-MU with variational approximated optimum model order NMF2D. IEEE Trans. Audio Speech Lang. Process. 75(1), 35–49 (2016)Google Scholar
  4. 4.
    C.E. Cherry, Some experiments on the recognition of speech, with one and with two ears. J. Acoust. Soc. Am. 25(5), 975–979 (1953)Google Scholar
  5. 5.
    A. Cichocki, R. Zdunek, S.I. Amari, Csiszár’s divergences for non-negative matrix factorization: family of new algorithms. In Proc. Int. Conf. Ind. Compon. Anal. Blind Signal Separat. (ICABSS’06), vol. 3889 (Charleston, SC, 2006), pp. 32–39Google Scholar
  6. 6.
    R. de Frein, S. Rickard, The synchronized short-time-Fourier-transform: properties and definitions for multichannel source separation. IEEE Trans. Signal Process. 59(1), 91–103 (2011)MathSciNetzbMATHGoogle Scholar
  7. 7.
    C. Févotte, A. Ozerov, Notes on nonnegative tensor factorization of the spectrogram for audio source separation: statistical insights and towards self-clustering of the spatial cues. In 7th International Symposium on Computer Music Modeling and Retrieval, (CMMR 2010) (2010)Google Scholar
  8. 8.
    C. Févotte, N. Bertin, J.-L. Durrieu, Nonnegative matrix factorization with the Itakura–Saito divergence With application to music analysis. Neural Comput. 21, 793–830 (2009)zbMATHGoogle Scholar
  9. 9.
    D. FitzGerald, M. Cranitch, E. Coyle, Non-negative tensor factorization for sound source separation. In Irish Signals and Systems Conf. Dublin, Ireland, (2005)Google Scholar
  10. 10.
    B. Gao, W.L. Woo, S.S. Dlay, Variational regularized 2-D nonnegative matrix factorization. IEEE Trans. Neural Netw. 23(5), 703–716 (2012)Google Scholar
  11. 11.
    B. Gao, W.L. Woo, S.S. Dlay, Unsupervised single-channel separation of nonstationary signals using Gammatone filterbank and Itakura–Saito nonnegative matrix two-dimensional factorizations. IEEE Trans. Circuits Syst. 60(3), 662–675 (2013)MathSciNetGoogle Scholar
  12. 12.
    S. Ge, J. Han, M. Han, Nonnegative mixture for underdetermined blind source separation based on a tensor algorithm. Circuits Syst. Signal Process. 34(9), 2935–2950 (2015)MathSciNetzbMATHGoogle Scholar
  13. 13.
    M. Goto, H. Hashiguchi, T. Nishimura, R. Oka, RWC music database: music genre database and musical instrument sound database. In Proc. Int. Sym. Music Inf. Retrieval (ISMIR), Baltimore (2003), pp. 229–230Google Scholar
  14. 14.
    Y. Guo, G.R. Naik, H. Nguyen, Single channel blind source separation based local mean decomposition for Biomedical applications. In Proc. IEEE 35th Annual Int. Conf. Engineering in Medicine and Biology Society (EMBC) (2013), pp 6812–6815Google Scholar
  15. 15.
    H. Guo, X. Li, L. Zhou, Z. Wu, Single-channel speech separation using dictionary-updated orthogonal matching pursuit and temporal structure information. Circuits Syst. Signal Process. 34(12), 3861–3882 (2015)MathSciNetGoogle Scholar
  16. 16.
    M. Harva, A. Kabán, Variational learning for rectified factor analysis. Signal Process. 87(3), 509–527 (2007)zbMATHGoogle Scholar
  17. 17.
    K.E. Hild II, H.T. Attias, S.S. Nagarajan, An expectation–maximization method for spatio–temporal blind source separation using an AR-MOG source model. IEEE Trans. Neural Netw. 19(3), 508–519 (2008)zbMATHGoogle Scholar
  18. 18.
    K. Hu, D.L. Wang, Unvoiced speech separation from nonspeech interference via CASA and spectral subtraction. IEEE Trans. Audio Speech Lang. Process. 19(6), 1600–1609 (2011)Google Scholar
  19. 19.
    A. Hyvärinen, Fast and robust fixed-point algorithms for independent component analysis. IEEE Trans. Neural Netw. 10(3), 626–634 (1999)Google Scholar
  20. 20.
    S. Kim, C.D. Yoo, Underdetermined blind source separation based on subspace representation. IEEE Trans. Signal Process. 57(7), 2604–2614 (2009)MathSciNetzbMATHGoogle Scholar
  21. 21.
    D. Kitamura, N. Ono, H. Sawada, H. Kameoka, H. Saruwatari, Determined blind source separation unifying independent vector analysis and nonnegative matrix factorization. IEEE Trans. Audio Speech Lang. Process. 24(9), 1626–1641 (2016)Google Scholar
  22. 22.
    R. Kompass, A generalized divergence measure for nonnegative matrix factorization. Neural Comput. 19(3), 780–791 (2007)MathSciNetzbMATHGoogle Scholar
  23. 23.
    V.A.C. Kumar, V.R. Rao, A. Dutta, Performance analysis of blind source separation using canonical correlation. Circuits Syst. Signal Process. 32, 1–16 (2017)Google Scholar
  24. 24.
    D.D. Lee, H.S. Seung, Learning the parts of objects with nonnegative matrix factorization. Nature 401, 788–791 (1999)zbMATHGoogle Scholar
  25. 25.
    D.D. Lee, H.S. Seung, Algorithms for non-negative matrix factorization. In Proc. NIPS (2000), pp. 556–562Google Scholar
  26. 26.
    C.J. Lin, On the convergence of multiplicative update algorithms for nonnegative matrix factorization. IEEE Trans. Neural Netw. 18(6), 1589–1596 (2007)Google Scholar
  27. 27.
    W. Lu, B.N. Zhang, Single channel time-varying amplitude LFM interference blind separation using MHMPSO particle filtering. In Proc. IEEE Int. Conf. Signal and Image Processing Applications (ICSIPA) (2013), pp. 425–430Google Scholar
  28. 28.
    G. Lu, M. Xiao, P. Wei, H. Zhang, A new method of blind source separation using single-channel ICA based on higher-order statistics. Math. Probl. Eng.. Article ID 439264 (2015)Google Scholar
  29. 29.
    D. Luengo, I. Santamaría, L. Vielva, C. Pantaleón Underdetermined blind separation of sparse sources with instantaneous and convolutive mixtures. In IEEE 13th Workshop on: Neural Networks for Signal Processing, NNSP’03. 2003,(2003), pp. 279–288Google Scholar
  30. 30.
    D. Luengo, I. Santamar´ıa, L. Vielva, A general solution to blind inverse problems for sparse input signals. Neurocomputing 69(1), 198–215 (2005)Google Scholar
  31. 31.
    A. Mansour, N. Benchekroun, C. Gervaise, Blind separation of underwater acoustic signals. In Proc. 6th International Conference on Independent Component Analysis and Blind Signal Separation (ICA’06), vol 3889 (2006), pp. 181–188Google Scholar
  32. 32.
    B. Mijovic, M. Vos, D. Gligorijevic, I.J. Taelman, S.V. Haffel, Source separation from single-channel recordings by combining empirical-mode decomposition and independent component analysis. IEEE Trans. Biomed. Eng. 57(9), 2188–2196 (2010)Google Scholar
  33. 33.
    M. Niknazar, H. Becker, B. Rivet, C. Jutten, P. Comon, Blind source separation of underdetermined mixtures of event-related sources. Sig. Process. 101, 52–64 (2014)Google Scholar
  34. 34.
    P. Paatero, U. Tapper, Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values. Environmetrics. 5(2), 111–126 (1994)Google Scholar
  35. 35.
    P. Parathai, W.L. Woo, S.S. Dlay, B. Gao, Single-channel blind separation using L1-sparse complex non-negative matrix factorization for acoustic signals. J. Acoust. Soc. Am. 137(1), 42–49 (2017)Google Scholar
  36. 36.
    T. Peng, Y. Chen, Z.W. Liu, Time-frequency domain blind source separation method for underdetermined instantaneous mixtures. Circuits Syst. Signal Process. 34(12), 3883–3895 (2015)MathSciNetGoogle Scholar
  37. 37.
    R.K. Prasad, H. Saruwatari, K. Shikano Single channel speech enhancement: MAP estimation using GGD prior under blind setup. In Proc. 5th International Conference on Independent Component Analysis and Blind Signal Separation (ICA’04), vol. 3195 (2004), pp. 873–880Google Scholar
  38. 38.
    R. Schachtner, G. Pöppel, A.M. Tomé, E.W. Lang, A Bayesian approach to the lee–seung update rules for nmf. Pattern Recogn. Lett. 45, 251–256 (2014)Google Scholar
  39. 39.
    Signal Separation Evaluation Campaign (SiSEC 2016). (2016). http://sisec.wiki.irisa.fr. Accessed 3 May (2017)
  40. 40.
    M.K. Su, T.D. Tan, J.O. Tobias, P. Gunnar, On the entropy computation of large complex gaussian mixture distributions. IEEE Trans. Signal Process. 63(17), 4710–4723 (2015)MathSciNetzbMATHGoogle Scholar
  41. 41.
    E. Vincent, R. Gribonval, C. Févotte, Performance measurement in blind audio source separation. IEEE Trans. Speech Audio Lang. Process. 14(4), 1462–1469 (2005)Google Scholar
  42. 42.
    F. Weninger, A. Lehmann, B. Schuller, OpenBliSSART: design and evaluation of a research toolkit for blind source separation in audio recognition tasks. In Proc. IEEE Int. Conf Acoustics, Speech and Signal Processing (ICASSP) (2011), 1625–1628Google Scholar
  43. 43.
    Y. Xiang, S.K. Ng, V.K. Nguyen, Blind separation of mutually correlated sources using precoders. IEEE Trans. Neural Netw. 21(1), 82–90 (2010)Google Scholar
  44. 44.
    S. Xie, L. Yang, J.-M. Yang, G. Zhou, Y. Xiang, Time-frequency approach to underdetermined blind source separation. IEEE Trans. Neural Netw. Learn. Syst. 23(2), 306–316 (2012)Google Scholar
  45. 45.
    Ö. Yilmaz, S. Rickard, Blind separation of speech mixtures via time-frequency masking. IEEE Trans. Signal Process. 52(7), 1830–1847 (2004)MathSciNetzbMATHGoogle Scholar
  46. 46.
    H. Zhu, S. Zhang, H. Zhao, Single-channel source separation of multi-component radar signal with the same generalized period using ICA. Circuits Syst. Signal Process. 35(1), 353–363 (2016)MathSciNetzbMATHGoogle Scholar
  47. 47.
    M. Zibulevsky, B.A. Pearlmutter, Blind source separation by sparse decomposition in a signal dictionary. Neural Comput. 13(4), 863–882 (2001)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Software EngineeringPayap UniversityChiang MaiThailand
  2. 2.Department of Computer and Information SciencesNorthumbria UniversityNewcastle upon TyneUK
  3. 3.School of Automation EngineeringUniversity of Electronic Science and Technology of ChinaChengduChina

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