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Underdetermined Reverberant Audio-Source Separation Through Improved Expectation–Maximization Algorithm

  • Yuan Xie
  • Kan Xie
  • Junjie Yang
  • Zongze Wu
  • Shengli XieEmail author
Short Paper
  • 27 Downloads

Abstract

Underdetermined reverberant audio-source separation is an important issue in speech and audio processing. To solve this problem, many separation algorithms have been proposed, in which model parameter estimation is performed in the time–frequency domain, leading to permutation ambiguity and poor separation performance. Additionally, in the existing expectation–maximization (EM) algorithms, one of the crucial problem is that updating the model parameters at each iterative step is time-consuming. In this paper, we present an improved EM algorithm that combines nonnegative matrix factorization (NMF) and time differences of arrival (TDOA) estimation, avoiding the time consumption by properly selecting initial values of the EM algorithm. In the proposed algorithm, NMF source model is used to avoid the permutation ambiguity problem, and acoustic localization can be achieved by transforming the TDOA. Then, model parameters are updated to obtain better separation results. Finally, the source signals are separated using Wiener filters. The experimental results show that compared with existing blind separation methods, the proposed algorithm achieves better performance on source separation.

Keywords

Underdetermined mixture Nonnegative matrix factorization Time differences of arrival Expectation–maximization 

Notes

Acknowledgements

The authors would like to thank the anonymous reviewers for their insightful comments and helpful critiques of the manuscript that helped improve this paper. This work was partially supported by the National Natural Science Foundation of China (Grants 613300032, 61773128, 61673126, U1701261). Additionally, this work was partially supported by the Postdoctoral Science Foundation of China, No. 2018M643022.

References

  1. 1.
    X. Alameda-Pineda, S. Gannot, D. Kounades-Bastian, L. Girin, R. Horaud, A variational EM algorithm for the separation of time-varying convolutive audio mixtures. IEEE/ACM Trans. Audio Speech Lang. Process. 24(8), 1408–1423 (2016)CrossRefGoogle Scholar
  2. 2.
    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 ACM Trans. Audio Speech Lang. Process. 25(1), 35–49 (2017)CrossRefGoogle Scholar
  3. 3.
    C. Blandin, A. Ozerov, E. Vincent, Multi-source TDOA estimation in reverberant audio using angular spectra and clustering. Signal Process. 91(10), 1950–1960 (2012)CrossRefGoogle Scholar
  4. 4.
    R. Chai, G. Naik, T.N. Nguyen, S. Ling, Y. Tran, A. Craig, H. Nguyen, Driver fatigue classification with independent component by entropy rate bound minimization analysis in an EEG-based system. IEEE J Biomed Health Inform 21(3), 715–724 (2017)CrossRefGoogle Scholar
  5. 5.
    Y. Chi, Guaranteed blind sparse spikes deconvolution via lifting and convex optimization. IEEE J. Select. Topics Signal Process. 10(4), 782–794 (2015)CrossRefGoogle Scholar
  6. 6.
    J. Cho, D.Y. Chang, Underdetermined convolutive BSS: Bayes risk minimization based on a mixture of super-Gaussian posterior approximation. IEEE/ACM Trans. Audio Speech Lang. Process. 23(5), 828–839 (2015)CrossRefGoogle Scholar
  7. 7.
    P. Comon, C. Jutten, Handbook of Blind Source Separation: Independent Component Analysis and Separation (Academic, Cambridge, 2010)Google Scholar
  8. 8.
    C.P. Demo, J. Srel, Cocktail Party Problem (Springer, New York, 2015)Google Scholar
  9. 9.
    S.C. Douglas, M. Gupta, H. Sawada, S. Makino, Spatiotemporal fastICA algorithms for the blind separation of convolutive mixtures. IEEE Trans. Audio Speech Lang. Process. 15(5), 1511–1520 (2007)CrossRefGoogle Scholar
  10. 10.
    N.Q.K. Duong, E. Vincent, Under-determined reverberant audio source separation using a full-rank spatial covariance model. IEEE Trans. Audio Speech Lang. Process. 18(7), 1830–1840 (2010)CrossRefGoogle Scholar
  11. 11.
    C. Fvotte, N. Bertin, J.L. Durrieu, Nonnegative matrix factorization with the Itakura–Saito divergence: with application to music analysis. Neural Comput. 21(3), 793 (2009)CrossRefGoogle Scholar
  12. 12.
    Y. Guo, G. R. Naik, H. Nguyen, Single channel blind source separation based local mean decomposition for biomedical applications, in Engineering in Medicine and Biology Society 2013, pp. 6812–6815Google Scholar
  13. 13.
    Y. Guo, S. Huang, Y. Li, G.R. Naik, Edge effect elimination in single-mixture blind source separation. Circuits Syst. Signal Process. 32(5), 2317–2334 (2013)MathSciNetCrossRefGoogle Scholar
  14. 14.
  15. 15.
    Y. Hu, P.C. Loizou, Evaluation of objective quality measures for speech enhancement. IEEE Trans. Audio Speech Lang. Process. 16(1), 229–238 (2008)CrossRefGoogle Scholar
  16. 16.
    D. Kitamura, N. Ono, H. Sawada, H. Kameoka, H. Saruwatari, Determined blind source separation unifying independent vector analysis and nonnegative matrix factorization. IEEE/ACM Trans. Audio Speech Lang. Process. 24(9), 1626–1641 (2016)CrossRefGoogle Scholar
  17. 17.
    H. Liu, S. Liu, T. Huang, Z. Zhang, Y. Hu, T. Zhang, Infrared spectrum blind deconvolution algorithm via learned dictionaries and sparse representation. Appl. Optics 55(10), 2813 (2016)CrossRefGoogle Scholar
  18. 18.
    G.R. Naik, S.E. Selvan, H.T. Nguyen, Single-channel EMG classification with ensemble-empirical-mode-decomposition-based ICA for diagnosing neuromuscular disorders. IEEE Trans. Neural Syst. Rehabil. Eng. 24(7), 734–743 (2016)CrossRefGoogle Scholar
  19. 19.
    G. Naik, A. Altimemy, H. Nguyen, Transradial amputee gesture classification using an optimal number of sEMG sensors: an approach using ICA clustering. IEEE Trans. Neural Syst. Rehabil. Eng. 24(8), 837–846 (2016)CrossRefGoogle Scholar
  20. 20.
    F. Nesta and M. Omologo, Convolutive underdetermined source separation through weighted interleaved ICA and spatio-temporal source correlation. In: International Conference on Latent Variable Analysis and Signal Separation, Lva/ica 2012, Tel Aviv, Israel, March 12–15, 2012. Proceedings, 2012, pp. 222–230Google Scholar
  21. 21.
    A. Ozerov, C. Fvotte, R. Blouet, J. L. Durrieu, Multichannel nonnegative tensor factorization with structured constraints for user-guided audio source separation. In: IEEE International Conference on Acoustics, Speech and Signal Processing, 2011, pp. 257–260Google Scholar
  22. 22.
    A. Ozerov, C. Fevotte, Multichannel nonnegative matrix factorization in convolutive mixtures for audio source separation. IEEE Trans. Audio Speech Lang. Process. 18(3), 550–563 (2010)CrossRefGoogle Scholar
  23. 23.
    G. Pendharkar, G.R. Naik, H.T. Nguyen, Using blind source separation on accelerometry data to analyze and distinguish the toe walking gait from normal gait in ITW children. Biomed. Signal Process. Control 13(5), 41–49 (2014)CrossRefGoogle Scholar
  24. 24.
    K. Rahbar, J.P. Reilly, A frequency domain method for blind source separation of convolutive audio mixtures. IEEE Trans. Speech Audio Process. 13(5), 832–844 (2005)CrossRefGoogle Scholar
  25. 25.
    H. Sawada, S. Araki, S. Makino, Underdetermined convolutive blind source separation via frequency bin-wise clustering and permutation alignment. IEEE Trans. Audio Speech Lang. Process. 19(3), 516–527 (2010)CrossRefGoogle Scholar
  26. 26.
    H. Sawada, H. Kameoka, S. Araki, N. Ueda, Multichannel extensions of non-negative matrix factorization with complex-valued data. IEEE Trans. Audio Speech Lang. Process. 21(5), 971–982 (2013)CrossRefGoogle Scholar
  27. 27.
    C.H. Taal, R.C. Hendriks, R. Heusdens, J. Jensen, An algorithm for intelligibility prediction of timefrequency weighted noisy speech. IEEE Trans. Audio Speech Lang. Process. 19(7), 2125–2136 (2011)CrossRefGoogle Scholar
  28. 28.
    E. Vincent, R. Gribonval, C. Fevotte, Performance measurement in blind audio source separation. IEEE Trans. Audio Speech Lang. Process. 14(4), 1462–1469 (2006)CrossRefGoogle Scholar
  29. 29.
    L. Wang, Y. Chi, Blind deconvolution from multiple sparse inputs. IEEE Signal Process. Lett. 23(10), 1384–1388 (2016)CrossRefGoogle Scholar
  30. 30.
    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)CrossRefGoogle Scholar
  31. 31.
    Y. Xie, K. Xie, J. Yang, S. Xie, Underdetermined blind source separation combining tensor decomposition and nonnegative matrix factorization. Symmetry 10(10), 521 (2018)CrossRefGoogle Scholar
  32. 32.
    J.-J. Yang, H.-L. Liu, Blind identification of the underdetermined mixing matrix based on k-weighted hyperline clustering. Neurocomputing 149(PB), 483–489 (2015)CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  • Yuan Xie
    • 1
  • Kan Xie
    • 1
  • Junjie Yang
    • 1
  • Zongze Wu
    • 1
  • Shengli Xie
    • 1
    Email author
  1. 1.Guangdong University of TechnologyGuangzhouChina

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