Skip to main content

Subband-Based Blind Source Separation and Permutation Alignment

  • Chapter
  • First Online:
Blind Source Separation

Part of the book series: Signals and Communication Technology ((SCT))

  • 2802 Accesses

Abstract

The aim of this chapter is to present the fundamental ideas of subband-based convolutive blind source separation (BSS) employing filter banks, in particular with a focus on the inherent permutation alignment problem associated with this approach, and bring attention to the most recent developments in this area, including the joint BSS approach in solving the convolutive mixing problem.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Akansu, A., Haddad, R.: Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets. Academic Press, Boston (1992)

    MATH  Google Scholar 

  2. Amari, S.: Natural gradient works efficiently in learning. Neural Comput. 10, 251–276 (1998)

    Article  Google Scholar 

  3. Amari, S., Douglas, S., Cichocki, A., Yang, H.: Multichannel blind deconvolution and equalization using the natural gradient. In: First IEEE Signal Processing Workshop on Signal Processing Advances in, Wireless Communications, pp. 101–104 (1997)

    Google Scholar 

  4. Bell, A.J., Sejnowski, T.J.: An information-maximization approach to blind separation and blind deconvolution. Neural Comput. 7(6), 1129–1159 (1995)

    Article  Google Scholar 

  5. Bellanger, M., Daguet, J.: TDM-FDM transmultiplexer: digital polyphase and FFT. IEEE Trans. Commun. 22(9), 1199–1205 (1974)

    Article  Google Scholar 

  6. Chan, S.C., Liu, W., Ho, K.L.: Multiplier-less perfect reconstruction modulated filter banks with sum-of-powers-of-two coefficients. IEEE Signal Process. Lett. 8, 163–166 (2001)

    Google Scholar 

  7. Cichocki, A., Amari, S.: Adaptive Blind Signal and Image Processing. Wiley, New York (2003)

    Google Scholar 

  8. Comon, P.: Independent component analysis, a new concept? Signal Process. 36(3), 287–314 (1994)

    Article  MATH  Google Scholar 

  9. Crochiere, R.E., Rabiner, L.R.: Multirate Digital Signal Processing. Prentice Hall, Englewood Cliffs (1983)

    Google Scholar 

  10. Douglas, S., Gupta, M.: Scaled natural gradient algorithms for instantaneous and convolutive blind source separation. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 2, pp. II-637–640 (2007)

    Google Scholar 

  11. Grbic, N., Tao, X.J., Nordholm, S., Claesson, I.: Blind signal separation using overcomplete subband representation. IEEE Trans. Speech Audio Process. 9(5), 524–533 (2001)

    Article  Google Scholar 

  12. Harteneck, M., Weiss, S., Stewart, R.W.: Design of near perfect reconstruction oversampled filter banks for subband adaptive filters. IEEE Trans. Circuits Syst. II: Analog Digital Signal Process. 46, 1081–1085 (1999)

    Google Scholar 

  13. Hotelling, H.: Relations between two sets of variates. Biometrika 28(3–4), 321–377 (1936)

    Article  MATH  Google Scholar 

  14. Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. Wiley, New York (2001)

    Book  Google Scholar 

  15. Hyvärinen, A., Oja, E.: A fast fixed-point algorithm for independent component analysis. Neural Comput. 9, 1483–1492 (1997)

    Article  Google Scholar 

  16. Ikram, M., Morgan, D.: Exploring permutation inconsistency in blind separation of speech signals in a reverberant environment. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 2, pp. 1041–1044. Istanbul, Turkey (2000)

    Google Scholar 

  17. Ikram, M., Morgan, D.: Permutation inconsistency in blind speech separation: investigation and solutions. IEEE Trans. Speech Audio Process. 13(1), 1–13 (2005)

    Article  Google Scholar 

  18. Karp, T., Fliege, N.: Modified DFT filter banks with perfect reconstruction. IEEE Trans. Circuits Syst. II: Analog Digital Signal Process. 46(11), 1404–1414 (1999)

    Article  MATH  Google Scholar 

  19. Kettenring, J.R.: Canonical analysis of several sets of variables. Biometrika 58(3), 433–451 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  20. Kim, T.: Real-time independent vector analysis for convolutive blind source separation. IEEE Trans. Circuits Syst. I Regul. Pap. 57(7), 1431–1438 (2010)

    Article  MathSciNet  Google Scholar 

  21. Kim, T., Attias, H.T., Lee, S.Y., Lee, T.W.: Blind source separation exploiting higher-order frequency dependencies. IEEE Trans. Audio Speech Lang. Process. 15(1), 70–79 (2007)

    Article  Google Scholar 

  22. Kim, T., Lee, I., Lee, T.W.: Independent vector analysis: definition and algorithms. In: Fortieth Asilomar Conference on Signals, Systems and Computers (ACSSC’06), pp. 1393–1396 (2006)

    Google Scholar 

  23. Kurita, S., Saruwatari, H., Kajita, S., Takeda, K., Itakura, F.: Evaluation of blind signal separation method using directivity pattern under reverberant conditions. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP’00), vol. 5, pp. 3140–3143 (2000)

    Google Scholar 

  24. Lee, J.H., Lee, T.W., Jolesz, F.A., Yoo, S.S.: Independent vector analysis (IVA): multivariate approach for fMRI group study. NeuroImage 40(1), 86–109 (2008)

    Article  Google Scholar 

  25. Lee, K.A., Gan, W.S.: On the subband orthogonality of cosine-modulated filter banks. IEEE Trans. Circuits Syst. II Express Briefs 53(8), 677–681 (2006)

    Article  Google Scholar 

  26. Lee, K.A., Gan, W.S., Kuo, S.M.: Subband Adaptive Filtering: Theory and Implementation. Wiley, New York (2009)

    Book  Google Scholar 

  27. Li, X.L., Adalı, T., Anderson, M.: Joint blind source separation by generalized joint diagonalization of cumulant matrices. Signal Process. 91(10), 2314–2322 (2011)

    Article  MATH  Google Scholar 

  28. Li, Y.O., Adalı, T., Wang, W., Calhoun, V.D.: Joint blind source separation by multi-set canonical correlation analysis. IEEE Trans. Signal Process. 57(10), 3918–3929 (2009)

    Google Scholar 

  29. Li, Y.O., Eichele, T., Calhoun, V., Adalı, T.: Group study of simulated driving fMRI data by multiset canonical correlation analysis. J. Signal Process. Syst. 68(1), 31–48 (2012)

    Google Scholar 

  30. Liu, W.: Blind beamforming for multi-path wideband signals based on frequency invariant transformation. In: Proceedings of the International Symposium on Communications, Control and Signal Processing (ISCCSP). Limassol, Cyprus (2010)

    Google Scholar 

  31. Liu, W.: Wideband beamforming for multi-path signals based on frequency invariant transformation. Int. J. Autom. Comput. 9, 420–428 (2012)

    Article  Google Scholar 

  32. Liu, W., Mandic, D.P.: Semi-blind source separation for convolutive mixtures based on frequency invariant transformation. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 5, pp. 285–288. Philadelphia, USA (2005)

    Google Scholar 

  33. Liu, W., Mandic, D.P., Cichocki, A.: A class of novel blind source extraction algorithms based on a linear predictor. In: Proceedings of IEEE International Symposium on Circuits and Systems, pp. 3599–3602. Kobe, Japan (2005)

    Google Scholar 

  34. Liu, W., Mandic, D.P., Cichocki, A.: Blind second-order source extraction of instantaneous noisy mixtures. IEEE Trans. Circuits Syst. II Express Briefs 53(9), 931–935 (2006)

    Article  Google Scholar 

  35. Liu, W., Mandic, D.P., Cichocki, A.: Blind source extraction of instantaneous noisy mixtures using a linear predictor. In: Proceedings of IEEE International Symposium on Circuits and Systems, pp. 4199–4202. Kos, Greece (2006)

    Google Scholar 

  36. Liu, W., Mandic, D.P., Cichocki, A.: Analysis and online realization of the cca approach for blind source separation. IEEE Trans. Neural Networks 18(5), 1505–1510 (2007)

    Article  Google Scholar 

  37. Liu, W., Mandic, D.P., Cichocki, A.: Blind source extraction based on a linear predictor. IET Signal Process. 1(1), 29–34 (2007)

    Article  Google Scholar 

  38. Liu, W., Mandic, D.P., Cichocki, A.: Blind source separation based on generalised canonical correlation analysis and its adaptive realization. In: Proceedings of International Congress on Image and Signal Processing, vol. 5, pp. 417–421. Hainan, China (2008)

    Google Scholar 

  39. Liu, W., Mandic, D.P., Cichocki, A.: A dual-linear predictor approach to blind source extraction for noisy mixtures. In: Proceedings of IEEE Workshop on Sensor Array and Multichannel Signal Processing, pp. 515–519. Darmstadt, Germany (2008)

    Google Scholar 

  40. Liu, W., Weiss, S.: Wideband Beamforming: Concepts and Techniqeus. Wiley, Chichester, UK (2010)

    Book  Google Scholar 

  41. Low, S.Y., Nordholm, S., Togneri, R.: Convolutive blind signal separation with post-processing. IEEE Trans. Speech Audio Process. 12(5), 539–548 (2004)

    Article  Google Scholar 

  42. Mazur, R., Mertins, A.: An approach for solving the permutation problem of convolutive blind source separation based on statistical signal models. IEEE Trans. Acoustics Speech Lang. Process. 17(1), 117–126 (2009)

    Article  Google Scholar 

  43. Murata, N., Ikeda, S., Ziehe, A.: An approach to blind source separation based on temporal structure of speech signals. Neurocomputing 41(1–4), 1–24 (2001)

    Article  MATH  Google Scholar 

  44. Park, H.M., Dhir, C.S., Oh, S.H., Lee, S.Y.: A filter bank approach to independent component analysis for convolved mixtures. Neurocomputing 69(16–18), 2065–2077 (2006)

    Article  Google Scholar 

  45. Peng, B., Liu, W., Mandic, D.P.: An improved solution to the subband blind source separation permutation problem based on optimized filter banks. In: Proceedings of the International Symposium on Communications, Control and Signal Processing, pp. 1–4. Limassol, Cyprus (2010)

    Google Scholar 

  46. Peng, B., Liu, W., Mandic, D.P.: Novel design of oversampled GDFT filter banks for application to subband based blind source separation. In: Proceedings of the IEEE Statistical Signal Processing Workshop (SSP), pp. 637–640. Nice, France (2011)

    Google Scholar 

  47. Peng, B., Liu, W., Mandic, D.P.: Reducing permutation error in subband-based convolutive blind separation. IET Signal Process. 6(1), 34–44 (2012)

    Article  MathSciNet  Google Scholar 

  48. Peng, B., Liu, W., Mandic, D.P.: Design of oversampled generalised discrete fourier transform filter banks for application to subband-based blind source separation. IET Signal Process. 7(9), 843–853 (2013)

    Article  Google Scholar 

  49. Peng, B., Liu, W., Mandic, D.P.: Subband-based joint blind source separation for convolutive mixtures employing m-cca. In: Proceedings of the Constantinides International Workshop on Signal Processing. London, UK (2013)

    Google Scholar 

  50. Ramstad, T.A., Tanem, J.P.: Cosine-modulated analysis-synthesis filterbank with critical sampling and perfect reconstruction. In: Proceedings IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 3, pp. 1789–1792 (1991)

    Google Scholar 

  51. Saruwatari, H., Kawamura, T., Shikano, K.: Blind source separation based on fast-convergence algorithm using ica and array signal processing. IEEE Trans. Audio Speech Lang. Process. 14, 666–678 (2001)

    Article  Google Scholar 

  52. Sathe, V., Vaidyanathan, P.: Effects of multirate systems on the statistical properties of random signals. IEEE Trans. Signal Process. 41(1), 131 (1993).

    Google Scholar 

  53. Sawada, H., Araki, S., Makino, S.: Measuring dependence of bin-wise separated signals for permutation alignment in frequency-domain BSS. In: IEEE International Symposium on Circuits and Systems (ISCAS 2007), pp. 3247–3250 (2007)

    Google Scholar 

  54. Sawada, H., Araki, S., Makino, S.: Underdetermined convolutive blind source separation via frequency bin-wise clustering and permutation alignment. IEEE Trans. Audio Speech Lang. Process. 19(3), 516–527 (2011)

    Article  Google Scholar 

  55. Sawada, H., Mukai, R., Araki, S., Makino, S.: Polar coordinate based nonlinear function for frequency-domain blind source separation. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 1, pp. I-1001–I-1004 (2002)

    Google Scholar 

  56. Sawada, H., Mukai, R., Araki, S., Makino, S.: A robust and precise method for solving the permutation problem of frequency-domain blind source separation. IEEE Trans. Speech Audio Process. 12(5), 530–538 (2004)

    Article  Google Scholar 

  57. Smaragdis, P.: Blind separation of convolved mixtures in the frequency domain. Neurocomputing 22(1–3), 21–34 (1998)

    Article  MATH  Google Scholar 

  58. Vaidyanathan, P.P.: Multirate Systems and Filter Banks. Prentice Hall, Englewood Cliffs (1993)

    MATH  Google Scholar 

  59. Vinjamuri, R., Crammond, D., Kondziolka, D., Lee, H.N., Mao, Z.H.: Extraction of sources of tremor in hand movements of patients with movement disorders. IEEE Trans. Inf. Technol. Biomed. 13(1), 49–56 (2009)

    Article  Google Scholar 

  60. Wang, L., Ding, H., Yin, F.: A region-growing permutation alignment approach in frequency-domain blind source separation of speech mixtures. IEEE Trans. Audio Speech Lang. Process. 19(3), 549–557 (2011)

    Article  Google Scholar 

  61. Wang, W., Sanei, S., Chambers, J.: Penalty function based joint diagonalisation approach for convolutive blind separation of nonstationary sources. IEEE Trans. Signal Process. 53(5), 1654–1669 (2005)

    Article  MathSciNet  Google Scholar 

  62. Weiss, S., Stewart, R.W.: On Adaptive Filtering in Oversampled Subbands. Shaker Verlag, Aachen (1998)

    Google Scholar 

  63. Weiss, S., Stewart, R.W., Stenger, A., Rabenstein, R.: Performance limitations of subband adaptive filters. In: Proceedings of EUSIPCO, vol. III, pp. 1245–1248 (1998)

    Google Scholar 

  64. Wilbur, M.R., Davidson, T.N., Reilly, J.P.: Efficient design of oversampled NPR GDFT filterbanks. IEEE Trans. Signal Process. 52(7), 1947–1963 (2004)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bo Peng .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Peng, B., Liu, W. (2014). Subband-Based Blind Source Separation and Permutation Alignment. In: Naik, G., Wang, W. (eds) Blind Source Separation. Signals and Communication Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55016-4_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-55016-4_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-55015-7

  • Online ISBN: 978-3-642-55016-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics