Skip to main content
SpringerLink
Log in

Gradient Adaptive Paraunitary Filter Banks for Spatio-Temporal Subspace Analysis and Multichannel Blind Deconvolution

  • Published:
Journal of VLSI signal processing systems for signal, image and video technology Aims and scope Submit manuscript

Abstract

Paraunitary filter banks are important for several signal processing tasks, including coding, multichannel deconvolution and equalization, adaptive beamforming, and subspace processing. In this paper, we consider the task of adapting the impulse response of a multichannel paraunitary filter bank via gradient ascent or descent on a chosen cost function. Our methods are spatio-temporal generalizations of gradient techniques on the Grassmann and Stiefel manifolds, and we prove that they inherently maintain the paraunitariness of the multichannel adaptive system over time. We then discuss the necessary practical approximations, modifications, and simplifications of the methods for solving two relevant signal processing tasks: (i) spatio-temporal subspace analysis and (ii) multichannel blind deconvolution. Simulations indicate that our methods can provide simple, useful solutions to these important problems.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P.P. Vaidyanathan, Multirate Systems and Filter Banks, Englewood Cliffs, NJ: Prentice-Hall, 1993.

    MATH  Google Scholar 

  2. D.T.M. Slock, “Blind Fractionally-Spaced Equalization, Perfect-Reconstruction Filter Banks, and Multichannel Linear Prediction,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, Adelaide, Australia, vol. 4, 1994, pp. 585-588.

    Google Scholar 

  3. M.K. Tsatsanis and G.B. Giannakis, “Principal Component Filter Banks for Optimum Multiresolution Analysis,” IEEE Trans. Signal Processing, vol. 43, 1995, pp. 1766-1777.

    Article  Google Scholar 

  4. A. Kiraç and P.P. Vaidyanathan, “Theory and Design of Optimum FIR Compaction Filters,” IEEE Trans. Signal Processing, vol. 46, 1998, pp. 903-919.

    Article  Google Scholar 

  5. P. Moulin and M.K. Mthçak, “Theory and Design of Signal-Adapted FIR Paraunitary Filter Banks,” IEEE Trans. Signal Processing, vol. 46, 1998, pp. 920-929.

    Article  Google Scholar 

  6. B. Xuan and R.H. Bamberger, “FIR Principal Component Filter Banks,” IEEE Trans. Signal Processing, vol. 46, 1998, pp. 930-940.

    Article  Google Scholar 

  7. O.S. Jahromi, M.A. Masnadi-Shirazi, and M. Fu, “A Fast O(N) Algorithm for Adaptive Filter Bank Design,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, Seattle, WA, vol. 3, 1998, pp. 1325-1328.

    Google Scholar 

  8. B. Porat and B. Friedlander, “Estimation of Spatial and Spectral Parameters of Multiple Sources,” IEEE Trans. Inform. Theory, vol. 29, 1983, pp. 412-425.

    Article  MATH  Google Scholar 

  9. B. Ottersten and T. Kailath, “Direction-of-Arrival Estimation for Wideband Sources Using the ESPRIT Algorithm,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, 1990, pp. 317-327.

    Article  Google Scholar 

  10. P. Loubaton and P.A. Regalia, “Blind Deconvolution of Multivariate Signals by Using Adaptive FIR Lossless Filters,” in Proc. EUSIPCO92, Brussels, Belgiumx, 1992, pp. 317-327.

  11. P.A. Regalia and P. Loubaton, “Rational Subspace Estimation Using Adaptive Lossless Filters,” IEEE Trans. Signal Processing, vol. 40, 1992, pp. 2392-2405.

    Article  MATH  Google Scholar 

  12. P.A. Regalia and D.-Y. Huang, “Attainable Error Bounds in Multirate Adaptive Lossless FIR Filters,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, vol. 2, Detroit, MI, 1995, pp. 1460-1463.

    Google Scholar 

  13. A. Benveniste, M. Goursat, and G. Ruget, “Robust Identification of a Nonminimum Phase System: Blind Adjustment of a Linear Equalizer in Data Communications,” IEEE Trans. Automat. Contr., vol. 25, 1980, pp. 385-399.

    Article  MathSciNet  MATH  Google Scholar 

  14. B. Farhang-Boroujeny and S. Nooshfar, “Adaptive Phase Equalization Using All-Pass Filters,” in Proc. IEEE Int. Conf. Commun., vol. 3, Denver, CO, 1991, pp. 1403-1407.

    Google Scholar 

  15. T. J. Lim and M.D. Macleod, “Adaptive Allpass Filtering for Nonminimum-Phase System Identification,” IEE Proc.—Vision, Image, Signal Processing, vol. 141, 1994, pp. 373-379.

    Article  Google Scholar 

  16. S. Hakyin (Ed.), Blind Deconvolution. Englewood Cliffs, NJ: Prentice-Hall, 1994.

    Google Scholar 

  17. P.A. McEwen and J.G. Kenney, “Allpass Forward Equalizer for Decision Feedback Equalization,” IEEE Trans. Magnetics, vol. 31, 1995, pp. 3045-3047.

    Article  Google Scholar 

  18. E. Abreu, S.K. Mitra, and R. Marchesani, “Nonminimum Phase Channel Equalization Using Noncausal Filters,” IEEE Trans. Signal Processing, vol. 45, 1997, pp. 1-13.

    Article  Google Scholar 

  19. S.C. Douglas and S.-Y. Kung, “Gradient Adaptive Algorithms for Contrast-Based Blind Deconvolution,” J. VLSI Signal Processing Syst., vol. 26, nos. 1/2, 2000, pp. 47-60.

    Article  MATH  Google Scholar 

  20. B. Widrow and E. Walach, Adaptive Inverse Control, Upper Saddle River, NJ: Prentice-Hall, 1996.

    Google Scholar 

  21. H.G. Grassmann, Die Ausdehnungslehre, Berlin: Enslin, 1862.

    Google Scholar 

  22. E. Stiefel, “Richtungsfelder und Fernparallelismus in n-Dimensionalem Manning Faltigkeiten,” Commentarii Math. Helvetici, vol. 8, 1935/1936, pp. 305-353.

    Article  MathSciNet  Google Scholar 

  23. E. Oja and J. Karhunen, “On Stochastic Approximation of the Eigenvectors and Eigenvalues of the Expectation of a Random Matrix,” J. Math Anal. Appl., vol. 106, no. 1, 1985, pp. 69-84.

    Article  MathSciNet  MATH  Google Scholar 

  24. L. Xu, “Least-Mean-Square Error Recognition Principle for Self-Organizing Neural Nets,” Neural Networks, vol. 6, 1993, pp. 627-648.

    Article  Google Scholar 

  25. S.T. Smith, “Geometric Optimization Methods for Adaptive Filtering,” Ph.D. thesis, Harvard Univ., Cambridge, MA, 1993.

  26. U. Helmke and J.B. Moore, Optimization and Dynamical Systems, New York: Springer-Verlag, 1994.

    Book  Google Scholar 

  27. D.R. Fuhrmann, “A Geometric Approach To Subspace Tracking,” in Proc. 31st Asilomar Conf. Signals, Syst., Comput., vol. 1, Pacific Grove, CA, 1997, pp. 783-787.

    Google Scholar 

  28. T.-P. Chen, S. Amari, and Q. Lin, “A Unified Algorithm for Principal and Minor Components Extraction,” Neural Networks, vol. 11, 1998, pp. 385-390.

    Article  Google Scholar 

  29. S.C. Douglas, S.-Y. Kung, and S. Amari, “A Self-Stabilized Minor Subspace Rule,” IEEE Signal Processing Lett., vol. 5, 1998, pp. 328-330.

    Article  Google Scholar 

  30. A. Edelman, T. Arias, and S.T. Smith, “The Geometry of Algorithms with Orthogonality Constraints,” Siam J. Matrix Anal. Appl., vol. 20, 1998, pp. 303-353.

    Article  MathSciNet  MATH  Google Scholar 

  31. K.I. Diamantaras and S.-Y. Kung, Principal Component Neural Networks, New York: Wiley, 1996.

    MATH  Google Scholar 

  32. S.C. Douglas, S. Amari, and S.Y. Kung, “On Gradient Adaptation with Unit-Norm Constraints,” IEEE Trans. Signal Processing, vol. 48, no. 6, 2000, pp. 1843-1847.

    Article  Google Scholar 

  33. P. Comon, “Independent Component Analysis: A New Concept?” Signal Processing, vol. 36, 1994, pp. 287-314.

    Article  MATH  Google Scholar 

  34. N. Delfosse and P. Loubaton, “Adaptive Blind Separation of Independent Sources: A Deflation Approach,” Signal Processing, vol. 45, 1995, pp. 59-83.

    Article  MATH  Google Scholar 

  35. S.-Y. Kung and C. Mejuto, “Extraction of Independent Components from Hybrid Mixture: KuicNet Learning Algorithm and Applications,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, vol. 2, Seattle, WA, 1998, pp. 1209-1212.

    Google Scholar 

  36. S.C. Douglas, “Self-Stabilized Gradient Algorithms for Blind Source Separation with Orthogonality Constraints,” IEEE Trans. Neural Networks, vol. 11, no. 6, 2000, pp. 1490-1497.

    Article  MATH  Google Scholar 

  37. S. Amari, “Natural Gradient Works Efficiently in Learning,” Neural Computation, vol. 10, 1998, pp. 251-276.

    Article  Google Scholar 

  38. S.C. Douglas and S. Amari, “Natural Gradient Adaptation,” in Unsupervised Adaptive Filtering, vol. I: Blind Source Separation, S. Haykin (Ed.), New York: Wiley, 2000, pp. 13-61.

    Google Scholar 

  39. R.H. Lambert, “Multichannel Blind Deconvolution: FIR Matrix Algebra and Separation of Multipath Mixtures,” Ph.D. thesis, University of Southern California, Los Angeles, CA, May 1996.

    Google Scholar 

  40. S.C. Douglas and S. Haykin, “On the Relationship Between Blind Deconvolution and Blind Source Separation,” in Proc. 31st Ann. Asilomar Conf. Signals, Syst., Comput., vol. 2, Pacific Grove, CA, 1997, pp. 1591-1595.

    Google Scholar 

  41. I. Sabala, A. Cichocki, and S. Amari, “Relationships Between Instantaneous Blind Source Separation and Multichannel Blind Deconvolution,” in Proc. IEEE Int. Joint Conf. Neural Networks, vol. 1, Anchorage, AK, 1998, pp. 39-44.

    Google Scholar 

  42. S.C. Douglas and S. Haykin, “Relationships Between Blind Deconvolution and Blind Source Separation,” in Unsupervised Adaptive Filtering, vol. II: Blind Deconvolution, S. Haykin (Ed.), New York: Wiley, 2000, pp. 113-145.

    Google Scholar 

  43. S.C. Douglas, A. Cichocki, and S. Amari, “Fast-Convergence Filtered Regressor Algorithms for Blind Equalisation,” Electron. Lett., vol. 32, no. 23, 1996, pp. 2114-2115.

    Article  Google Scholar 

  44. S.C. Douglas, A. Cichocki, and S. Amari, “Quasi-Newton Filtered-Error and Filtered-Regressor Algorithms for Adaptive Equalization and Deconvolution,” in Proc. 1st IEEE Workshop Signal Proc. Adv. Wireless Commun., Paris, France, 1997, pp. 109-112.

  45. S.C. Douglas, A. Cichocki, and S. Amari, “Self-Whitening Algorithms for Adaptive Equalization and Deconvolution,” IEEE Trans. Signal Processing, vol. 47, 1999, pp. 1161-1165.

    Article  Google Scholar 

  46. P. Comon, “Contrasts for Multichannel Blind Deconvolution,” IEEE Signal Processing Lett., vol. 3, 1996, pp. 209-211.

    Article  Google Scholar 

  47. E. Moreau and J.-C. Pesquet, “Generalized Contrasts for Multi-channel Blind Deconvolution of Linear Systems,” IEEE Signal Processing Lett., vol. 4, 1997, pp. 182-183.

    Article  Google Scholar 

  48. R.-W. Liu and Y. Inouye, “Direct Blind Signal Separation of Convolutive Mixtures of White Non-Gaussian Signals,” in Proc. 1st Int. Conf. Indep. Compon. Anal. Signal Sep., Aussois, France, 1999, pp. 233-238.

  49. A. Gorokhov and J.-F. Cardoso, “Equivariant Blind Deconvolution of MIMO-FIR Channels,” in Proc. 1st IEEE Workshop Signal Processing Adv. Wireless Commun., Paris, France, 1997, pp. 89-92.

  50. S. Amari, S.C. Douglas, A. Cichocki, and H.H. Yang, “Multichannel Blind Deconvolution Using the Natural Gradient,” in Proc. 1st IEEE Workshop Signal Proc. Adv. Wireless Commun., Paris, France, 1997, pp. 101-104.

  51. K. Torkkola, “Blind Separation of Convolved Sources Based on Information Maximization,” IEEE Workshop Neural Networks Signal Processing, Kyoto, Japan, 1996, pp. 423-432.

  52. R.H. Lambert and A.J. Bell, “Blind Separation of Multiple Speakers in a Multipath Environment,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, vol. 1, Munich, Germany, 1997, pp. 423-426.

    Google Scholar 

  53. S. Amari, S.C. Douglas, A. Cichocki, and H.H. Yang, “Novel On-Line Adaptive Learning Algorithms for Blind Deconvolution Using the Natural Gradient Approach,” in Proc. 11th Ifac Symp. Syst. Ident., vol. 3, Kitakyushu, Japan, 1997, pp. 1057-1062.

    Google Scholar 

  54. S.C. Douglas and A. Cichocki, “Neural Networks for Blind Decorrelation of Signals,” IEEE Trans. Signal Processing, vol. 45, 1997, pp. 2829-2842.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Southern Methodist University, Dallas, Texas, 75275, USA

    Scott C. Douglas

  2. Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Wako-shi, Saitama, 351-0198, Japan

    Shun-Ichi Amari

  3. Department of Electrical Engineering, Princeton University, Princeton, New Jersey, 08544, USA

    S.-Y. Kung

Authors
  1. Scott C. Douglas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shun-Ichi Amari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S.-Y. Kung
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Douglas, S.C., Amari, SI. & Kung, SY. Gradient Adaptive Paraunitary Filter Banks for Spatio-Temporal Subspace Analysis and Multichannel Blind Deconvolution. The Journal of VLSI Signal Processing-Systems for Signal, Image, and Video Technology 37, 247–261 (2004). https://doi.org/10.1023/B:VLSI.0000027489.11890.2a

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:VLSI.0000027489.11890.2a

Search

Navigation