Skip to main content

Blind Separation of Nonstationary Sources Based on Spatial Time-Frequency Distributions

Abstract

Blind source separation (BSS) based on spatial time-frequency distributions (STFDs) provides improved performance over blind source separation methods based on second-order statistics, when dealing with signals that are localized in the time-frequency (t-f) domain. In this paper, we propose the use of STFD matrices for both whitening and recovery of the mixing matrix, which are two stages commonly required in many BSS methods, to provide robust BSS performance to noise. In addition, a simple method is proposed to select the auto- and cross-term regions of time-frequency distribution (TFD). To further improve the BSS performance, t-f grouping techniques are introduced to reduce the number of signals under consideration, and to allow the receiver array to separate more sources than the number of array sensors, provided that the sources have disjoint t-f signatures. With the use of one or more techniques proposed in this paper, improved performance of blind separation of nonstationary signals can be achieved.

References

  1. 1.

    Tong L, Inouye Y, Liu R-W: Waveform-preserving blind estimation of multiple independent sources. IEEE Transactions on Signal Processing 1993, 41(7):2461–2470. 10.1109/78.224254

    Article  Google Scholar 

  2. 2.

    Cardoso JF, Souloumiac A: Blind beamforming for non-Gaussian signals. IEE Proceedings, Part F: Radar and Signal Processing 1993, 140(6):362–370. 10.1049/ip-f-2.1993.0054

    Google Scholar 

  3. 3.

    Belouchrani A, Abed-Meraim K, Cardoso J-F, Moulines E: Blind source separation technique using second-order statistics. IEEE Transactions on Signal Processing 1997, 45(2):434–444. 10.1109/78.554307

    Article  Google Scholar 

  4. 4.

    Grellier O, Comon P: Blind separation of discrete sources. IEEE Signal Processing Letters 1998, 5(8):212–214. 10.1109/97.704975

    Article  Google Scholar 

  5. 5.

    Chen B, Petropulu AP: Frequency domain blind MIMO system identification based on second- and higher order statistics. IEEE Transactions on Signal Processing 2001, 49(8):1677–1688. 10.1109/78.934137

    Article  Google Scholar 

  6. 6.

    Hyvärinen A, Karhunen J, Oja E: Independent Component Analysis. John Wiley & Sons, New York, NY, USA; 2001.

    Google Scholar 

  7. 7.

    Hyvärinen A: Survey on independent component analysis. Neural Computing Surveys 1999, 2: 94–128.

    Google Scholar 

  8. 8.

    O'Grady PD, Pearlmutter BA, Rickard ST: Survey of sparse and non-sparse methods in source separation. International Journal of Imaging Systems and Technology 2005, 15(1):18–33. special issue on Blind Source Separation and Deconvolution in Imaging and Image Processing 10.1002/ima.20035

    Article  Google Scholar 

  9. 9.

    Chen V, Ling H: Time-Frequency Transforms for Radar Imaging and Signal Analysis. Artech House, Boston, Mass, USA; 2002.

    Google Scholar 

  10. 10.

    Boashash B (Ed): Time-Frequency Signal Analysis and Processing. Elsevier, Oxford, UK; 2003.

    Google Scholar 

  11. 11.

    Debnath L (Ed): Wavelets and Signal Processing. Birkhäuser, Boston, Mass, USA; 2003.

    Google Scholar 

  12. 12.

    Belouchrani A, Amin MG: Blind source separation based on time-frequency signal representations. IEEE Transactions on Signal Processing 1998, 46(11):2888–2897. 10.1109/78.726803

    Article  Google Scholar 

  13. 13.

    Leyman AR, Kamran ZM, Abed-Meraim K: Higher-order time frequency-based blind source separation technique. IEEE Signal Processing Letters 2000, 7(7):193–196. 10.1109/97.847366

    Article  Google Scholar 

  14. 14.

    Belouchrani A, Abed-Meraim K, Amin MG, Zoubir AM: Joint anti-diagonalization for blind source separation. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '01), May 2001, Salt Lake, Utah, USA 5: 2789–2792.

    Google Scholar 

  15. 15.

    Giulieri L, Thirion-Moreau N, Arquès P-Y: Blind sources separation based on bilinear time-frequency representations: a performance analysis. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '02), May 2002, Orlando, Fla, USA 2: 1649–1652.

    Google Scholar 

  16. 16.

    Févotte C, Doncarli C: Two contributions to blind source separation using time-frequency distributions. IEEE Signal Processing Letters 2004, 11(3):386–389. 10.1109/LSP.2003.819343

    Article  Google Scholar 

  17. 17.

    Linh-Trung N, Belouchrani A, Abed-Meraim K, Boashash B: Separating more sources than sensors using time-frequency distributions. EURASIP Journal on Applied Signal Processing 2005, 2005(17):2828–2847. 10.1155/ASP.2005.2828

    MATH  Google Scholar 

  18. 18.

    Mu W, Amin MG, Zhang Y: Bilinear signal synthesis in array processing. IEEE Transactions on Signal Processing 2003, 51(1):90–100. 10.1109/TSP.2002.806577

    MathSciNet  Article  Google Scholar 

  19. 19.

    Yilmaz Ö, Rickard S: Blind separation of speech mixtures via time-frequency masking. IEEE Transactions on Signal Processing 2004, 52(7):1830–1847. 10.1109/TSP.2004.828896

    MathSciNet  Article  Google Scholar 

  20. 20.

    Yeredor A: Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separation. IEEE Transactions on Signal Processing 2002, 50(7):1545–1553. 10.1109/TSP.2002.1011195

    MathSciNet  Article  Google Scholar 

  21. 21.

    Giulieri L, Thirion-Moreau N, Arquès P-Y: Blind sources separation based on quadratic time-frequency representations: a method without pre-whitening. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '03), April 2003, Hong Kong 5: 289–292.

    Google Scholar 

  22. 22.

    Bofill P, Zibulevsky M: Blind separation of more sources than mixtures using sparsity of their short-time Fourier transform. Proceedings of the 2nd International Workshop on Independent Component Analysis and Blind Signal Separation, June 2000, Helsinki, Finland 87–92.

    Google Scholar 

  23. 23.

    Aïssa-El-Bey A, Abed-Meraim K, Grenier Y: Underdetermined blind source separation of audio sources in time-frequency domain. Proceedings of the Signal Processing with Adaptive Sparse Structured Representations (SPARS '05), November 2005, Rennes, France

    Google Scholar 

  24. 24.

    Rickard S, Melia T, Fearon C: DESPRIT—histogram based blind source separation of more sources than sensors using subspace methods. Proceedings of IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA '05), October 2005, New Paltz, NY, USA 5–8.

    Google Scholar 

  25. 25.

    Cirillo LA, Amin MG: Auto-term detection using time-frequency array processing. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '03), April 2003, Hong Kong 6: 465–468.

    Google Scholar 

  26. 26.

    Zhang Y, Mu W, Amin MG: Subspace analysis of spatial time-frequency distribution matrices. IEEE Transactions on Signal Processing 2001, 49(4):747–759. 10.1109/78.912919

    Article  Google Scholar 

  27. 27.

    Holobar A, Fevotte C, Doncarli C, Zazula D: Single autoterms selection for blind source separation in time-frequency plane. Proceedings of 11th European Signal Processing Conference (EUSIPCO '02), September 2002, Toulouse, France 565–568.

    Google Scholar 

  28. 28.

    Zhang Y, Amin MG: Spatial averaging of time-frequency distributions for signal recovery in uniform linear arrays. IEEE Transactions on Signal Processing 2000, 48(10):2892–2902. 10.1109/78.869043

    MathSciNet  Article  Google Scholar 

  29. 29.

    Amin MG, Zhang Y: Direction finding based on spatial time-frequency distribution matrices. Digital Signal Processing 2000, 10(4):325–339. 10.1006/dspr.2000.0374

    Article  Google Scholar 

  30. 30.

    Zhang Y, Amin MG: Blind separation of sources based on their time-frequency signatures. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '00), June 2000, Istanbul, Turkey 5: 3132–3135.

    Google Scholar 

  31. 31.

    Zhang Y, Amin MG, Frazer GJ: A new approach to FM jammer suppression for digital communications. Proceedings of IEEE Sensor Array and Multichannel Signal Processing Workshop, August 2002, Rosslyn, Va, USA

    Google Scholar 

  32. 32.

    Boudreaux-Bartels GF, Parks TW: Time-varying filtering and signal estimation using Wigner distribution synthesis techniques. IEEE Transactions on Acoustics, Speech, and Signal Processing 1986, 34(3):442–451. 10.1109/TASSP.1986.1164833

    MathSciNet  Article  Google Scholar 

  33. 33.

    Krattenthaler W, Hlawatsch F: Time-frequency design and processing of signals via smoothed Wigner distributions. IEEE Transactions on Signal Processing 1993, 41(1):278–287. 10.1109/TSP.1993.193145

    Article  Google Scholar 

  34. 34.

    Hlawatsch F, Krattenthaler W: Bilinear signal synthesis. IEEE Transactions on Signal Processing 1992, 40(2):352–363. 10.1109/78.124945

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Yimin Zhang.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://doi.org/creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Zhang, Y., Amin, M.G. Blind Separation of Nonstationary Sources Based on Spatial Time-Frequency Distributions. EURASIP J. Adv. Signal Process. 2006, 064785 (2006). https://doi.org/10.1155/ASP/2006/64785

Download citation

Keywords

  • Information Technology
  • Quantum Information
  • Separation Method
  • Array Sensor
  • Source Separation