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A Mixing Matrix Estimation Algorithm for the Time-Delayed Mixing Model of the Underdetermined Blind Source Separation Problem

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Abstract

Considering the time-delayed mixing model of the underdetermined blind source separation problem, we propose a novel mixing matrix estimation algorithm in this paper. First, we introduce the short-time Fourier transform (STFT) to transform the mixed signals from the time domain to the time–frequency domain. Second, a neoteric transformation matrix is addressed to construct the linear clustering property of STFT coefficients. Then, a preeminent detection algorithm is raised to identify the single source points. After eliminating the low-energy points and outliers in the time–frequency domain, a potential function of clustering approach is put forward to cluster the single source points and obtain the clustering centers. Finally, the mixing matrix can be estimated through the derivation and calculation. The experimental results validate that the proposed algorithm not only accurately estimates the mixing matrix for the time-delayed mixing model of the underdetermined blind source separation problem but also has certain universality for different array structures. Therefore, both the effectiveness and superiority of the proposed algorithm have been verified.

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References

  1. T. Adali, Y. Levin-Schwartz, V.D. Calhoun, Multimodal data fusion using source separation: application to medical imaging. Proc. IEEE 103(9), 1494–1506 (2015)

    Article  Google Scholar 

  2. T. Dong, Y. Lei, J. Yang, An algorithm for underdetermined mixing matrix estimation. Neurocomputing 104, 26–34 (2013)

    Article  Google Scholar 

  3. J. Du, Y. Tu, L.R. Dai, A regression approach to single-channel speech separation via high-resolution deep neural networks. IEEE/ACM Trans. Audio Speech Lang. Process. 24(8), 1424–1437 (2016)

    Article  Google Scholar 

  4. R. Gribonval, S. Lesage, A survey of sparse component analysis for blind source separation: principles, perspectives, and new challenges, in ESANN’2006 Proceedings—European Symposium on Artificial Neural Networks ,Bruges (Belgium), pp. 26–28 (2006)

  5. Y.J. Gu, N.A. Goodman, Information-theoretic compressive sensing kernel optimization and Bayesian Cramer-Rao bound for time delay estimation. IEEE Trans. Signal Process. 65(17), 4525–4537 (2017)

    Article  MathSciNet  Google Scholar 

  6. A. Hyvarinen, Fast and robust fixed-point algorithms for independent component analysis. IEEE Trans. Neural Netw. 10(3), 626–634 (1999)

    Article  Google Scholar 

  7. Y. Jiang, J.P. Wu, C.Q. Zong, An effective diagnosis method for single and multiple defects detection in gearbox based on nonlinear feature selection and kernel-based extreme learning machine. J. Vibroeng. 16(1), 499–512 (2014)

    Google Scholar 

  8. S. Kim, C.D. Yoo, Underdetermined blind source separation based on subspace representation. IEEE Trans. Signal Process. 57(7), 2604–2614 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. H. Li, Y.H. Shen, J.G. Wang, Estimation of the complex-valued mixing matrix by single-source-points detection with less sensors than sources. Trans. Emerg. Telecommun. Technol. 23(2), 137–147 (2012)

    Article  Google Scholar 

  10. Y.B. Li, W. Nie, F. Ye, A mixing matrix estimation algorithm for underdetermined blind source separation. Circuits Systems Signal Process. 35(9), 3367–3379 (2016)

    Article  MathSciNet  Google Scholar 

  11. K. Mohanaprasad, P. Arulmozhivarman, Wavelet-based ICA using maximum likelihood estimation and information-theoretic measure for acoustic echo cancellation during double talk situation. Circuits Systems Signal Process. 34(12), 3915–3931 (2015)

    Article  MathSciNet  Google Scholar 

  12. A. Mustafi, S.K. Ghorai, A novel blind source separation technique using fractional Fourier transform for denoising medical images. Optik 124(3), 265–271 (2013)

    Article  Google Scholar 

  13. G.R. Naik, D.K. Kumar, An overview of independent component analysis and its applications. Informatica 35(1), 63–81 (2011)

    MATH  Google Scholar 

  14. F.M. Naini, G.H. Mohimani, M. Babaie-Zadeh, Estimating the mixing matrix in sparse component analysis (SCA) based on partial k-dimensional subspace clustering. Neurocomputing 71(10), 2330–2343 (2008)

    Article  Google Scholar 

  15. M. Puigt, Y. Deville, Time-frequency ratio-based blind separation methods for attenuated and time-delayed sources. Mech. Syst. Signal Process. 19(6), 1348–1379 (2005)

    Article  Google Scholar 

  16. S. Qin, J. Guo, C. Zhu, Sparse component analysis using time-frequency representations for operational modal analysis. Sensors 15(3), 6497–519 (2015)

    Article  Google Scholar 

  17. V.G. Reju, S.N. Koh, I.Y. Soon, An algorithm for mixing matrix estimation in instantaneous blind source separation. Signal Process. 89(9), 1762–1773 (2009)

    Article  MATH  Google Scholar 

  18. Z.G. Shi, C.W. Zhou, Y.J. Gu, Source estimation using coprime array: a sparse reconstruction perspective. IEEE Sens. J. 17(3), 755–765 (2017)

    Article  Google Scholar 

  19. J. Sun, Y. Li, J. Wen, Novel mixing matrix estimation approach in underdetermined blind source separation. Neurocomputing 173(P3), 623–632 (2016)

    Article  Google Scholar 

  20. R. Takeda, K. Nakadai, T. Takahashi, Efficient blind dereverberation and echo cancellation based on independent component analysis for actual acoustic signals. Neural Comput. 24(1), 234–272 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. J.J. Thiagarajan, K. Natesan Ramamurthy, A. Spanias, Mixing matrix estimation using discriminative clustering for blind source separation. Digital Signal Process. 23(1), 9–18 (2013)

    Article  MathSciNet  Google Scholar 

  22. O. Yilmaz, S. Rickard, Blind separation of speech mixtures via time-frequency masking. IEEE Trans. Signal Process. 52(7), 1830–1847 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  23. G. Yu, Fault feature extraction using independent component analysis with reference and its application on fault diagnosis of rotating machinery. Neural Comput. Appl. 26(1), 187–198 (2015)

    Article  Google Scholar 

  24. X.C. Yu, J.D. Xu, H. Dan, A new blind image source separation algorithm based on feedback sparse component analysis. Signal Process. 93(1), 288–296 (2013)

    Article  Google Scholar 

  25. H. Zayyani, M. Babaie-Zadeh, Approximated Cramer-Rao bound for estimating the mixing matrix in the two-sensor noisy sparse component analysis (SCA). Digital Signal Process. 23(3), 771–779 (2013)

    Article  MathSciNet  Google Scholar 

  26. H. Zayyani, M. Babaie-Zadeh, F. Haddadi, On the Cramer-Rao bound for estimating the mixing matrix in noisy sparse component analysis. IEEE Signal Process. Lett. 15, 609–612 (2008)

    Article  Google Scholar 

  27. H. Zayyani, M. Babaie-Zadeh, C. Jutten, An iterative Bayesian algorithm for sparse component analysis in presence of noise. IEEE Trans. Signal Process. 57(11), 4378–4390 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  28. L. Zhang, J. Yang, Z. Guo, Underdetermined blind source separation from time-delayed mixtures based on prior information exploitation. J. Electr. Eng. Technol. 10(5), 2179–2188 (2015)

    Article  Google Scholar 

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Acknowledgements

The paper is funded by the National Natural Science Foundation of China (No. 61701134), the Natural Science Foundation of Heilongjiang Province, China (No. F2017004), and the National Key Research and Development Program of China (No. 2016YFF0102806). Moreover, this work is supported by the Fundamental Research Funds for the Central Universities of China (Nos. HEUCFM180801, HEUCFM180802), and the Ph.D. Student Research and Innovation Fund of the Fundamental Research Funds for the Central Universities of China (No. HEUGIP201708).

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Authors and Affiliations

  1. College of Information and Communication Engineering, Harbin Engineering University, Harbin, 150001, China

    Fang Ye, Jie Chen, Lipeng Gao, Wei Nie & Qian Sun

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  1. Fang Ye
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  2. Jie Chen
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  3. Lipeng Gao
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  4. Wei Nie
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  5. Qian Sun
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Correspondence to Lipeng Gao.

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Ye, F., Chen, J., Gao, L. et al. A Mixing Matrix Estimation Algorithm for the Time-Delayed Mixing Model of the Underdetermined Blind Source Separation Problem. Circuits Syst Signal Process 38, 1889–1906 (2019). https://doi.org/10.1007/s00034-018-0930-5

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