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A unified balanced approach to multichannel blind deconvolution

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Abstract

In this paper, we explore the application of a common operator used in systems theory, viz., the delta operator, to formulate a unified theory of multichannel blind deconvolution (MBD) which is valid in both discrete and continuous time domains. Apart from providing a unified treatment of MBD problems, this formulation permits a smooth transition of the demixer from a discrete time domain to a continuous time domain when the sampling rate is high. Furthermore we give a unified treatment of a balanced parameterized state space formulation to solving the MBD problem in both discrete and continuous time domains when the number of states is unknown.

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References

  1. Cichocki A. and Amari S. (2002). Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications. Wiley, West Sussex

    Google Scholar 

  2. Haykin S. (1994). Blind Deconvolution. Prentice-Hall, New Jersey

    Google Scholar 

  3. Lambert, R.H.: Multichannel blind deconvolution: FIR matrix algebra and separation of multipath mixtures. PhD Thesis, University of Southern California (1996)

  4. Attias H. and Schreiner C.E. (1998). Blind source separation and deconvolution: the dynamic component analysis algorithm. Neural Comput. 10(6): 1373–1424

    Article  Google Scholar 

  5. Valpola H. and Karhunen J. (2002). An unsupervised ensemble learning method for nonlinear dynamic state-space models. Neural Comput. 14(11): 2647–2692

    Article  MATH  Google Scholar 

  6. Zhang, L., Amari, S., Cichocki, A.: Natural gradient approach to blind separation of over- and under-complete mixtures. In: Proceeding of the 1st International Workshop on Independent Component Analysis and Signal Separation, pp. 455–460 (1999)

  7. Zhang L. and Cichocki A. (2000). Blind deconvolution of dynamical systems: a state space approach. J. Signal Proces. 4(2): 111–130

    Google Scholar 

  8. Xia, B., Zhang, L.: Multichannel blind deconvolution of non- minimum phase system using cascade structure. In: The 11th International Conference on Neural Information Processing, ICONIP, pp. 1186–1191 (2004)

  9. Taylor, R.M. Jr, Mili, L., Zaghloul, A.I.: MOptimal multichannel blind deconvolution for parameterized channels and known source densities. Technical Report, Alexandria Research Institute of Virginia Tech (2005)

  10. Salam, F.M., Erten, G., Waheed, K.: Blind source recovery: algorithms for static and dynamic environments. In: NNS-IEEE International Joint Conference on Neural Networks, IJCNN (2001)

  11. Erten G. and Salam F. (1998). Voice extraction by on-line signal separation and recovery. IEEE Trans. on Circuits Systems II: Analog Digital Signal Proces. 46(7): 915–922

    Article  Google Scholar 

  12. Amari, S., Douglas, S., Cichocki, A., Yang, H.H.: Multichannel blind deconvolution and equalization using the natural gradient. In: Proceedings of IEEE International Workshop on Wireless Communication, pp. 101–104 (1997)

  13. Torkkola, K.: Blind deconvolution, information maximization, and recursive filters. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 21–24 (1997)

  14. Goodwin G.C., Middleton R.H. and Poor H.C. (1992). High-speed digital signal processing and control. Proc. IEEE 80(2): 240–259

    Article  Google Scholar 

  15. Middleton, R.H., Goodwin, G.C.: Digital Control and Estimation: A Unified Aprroach. Prentice Hall, Englewood Cliffs (1990)

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

    Article  MathSciNet  Google Scholar 

  17. Tsoi, A.C., Ma, L.S.: Blind deconvolution of dynamical system using a balanced parameterised state space approach. In: IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP, vol. 4, pp. 309–312 (2003)

  18. Glover K. (1984). All optimal hankel norm approximations of linear multivariable systems and L ∞ error bounds. International J. Control 39: 1115–1193

    Article  MATH  MathSciNet  Google Scholar 

  19. Chou C.T. and Maciejowski J.M. (1997). System Identification using balanced parametrizations. IEEE Trans. Autom. Control 42(7): 956–974

    Article  MATH  MathSciNet  Google Scholar 

  20. Nandi A.K. (1999). Blind Estimation Using Higher-Order Statistics. Kluwer, Dordrecht

    Google Scholar 

  21. Waheed, K., Salam, F.M.: A data-derived quadratic independence measure for adaptive blind source recovery in practical applications. In: 45th IEEE International Midwest Symposium on Circuits and Systems, vol. 3, pp. 473–476 (2002)

  22. Choudrey R.A.: Variational methods for Bayesian independent component analysis. PhD Thesis, University of Oxford (2002)

  23. Moddemeijer R. (1989). On estimation of entropy and mutual information of continuous distributions. Signal Proces. 16(3): 233–246

    Article  MathSciNet  Google Scholar 

  24. Strehl, A.: Relationship-based clustering and cluster ensembles for high-dimensional Data Mining. PhD Thesis, The University of Texas at Austin (2002)

  25. Newman M.J. and Holmes D.G. (2003). Delta operator digital filters for high performance inverter applocations. IEEE Trans. Power Electron. 18: 447–454

    Article  Google Scholar 

  26. Agoston A., Pepper S., Norton R., Ebner J. and Schoen K. (2003). 100GHz through-line sampler system with sampling rates in excess of 10 Gsamples/second. IEEE MTT-S Int. Microwave Symp. Digest 3: 519–1521

    Google Scholar 

  27. Moody, J., Wu, L.: Statistical analysis of tick-by-tick foreign exchange data. In: Proceedings of the High Frequency Data in Finance Conference, Zurich (1995)

  28. Breton, D., Deslagnes, E.: Very high dynamic range and high-sampling rate VME digitizing board for physics experiments. In: Proceedings 10TH Workshop on Electronics for LHC Experiments and Future Experiments, Boston (2004)

  29. Lee T.W. (1998). Independent Component Analysis: Theory and Applications. Kluwer, Dordrecht

    MATH  Google Scholar 

  30. Zhang L., Cichocki A. and Amari S. (1999). Natural gradient algorithm for blind separation of overdetermined mixture with additive noise. IEEE Signal Process. Lett. 6(11): 293–295

    Article  Google Scholar 

  31. MacKay D.J.C. (2003). Information Theory, Inference and Learning Algorithms. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  32. Choudrey, R.A., Roberts, S.J.: Flexible Bayesian independent component analysis for blind source separation. In: International Workshop on Independent Component Analysis and Blind Signal Separation (2001)

  33. Akaike, H.: Information theory and an extension of maximum likelihood principle. In: Proceedings of the Second International Symposium on Information Theory (1973)

  34. Raftery A.E. (1986). Choosing models for cross-classifications. Am. Sociol. Rev. 51: 145–146

    Article  Google Scholar 

  35. Rissanen J. (1978). Modeling by shortest data description. Automatica 14: 465–471

    Article  MATH  Google Scholar 

  36. Rissanen J. (1982). Estimation of structure by minimum description length. Circuits Systems Signal Process 1(3–4): 395–406

    Article  MATH  MathSciNet  Google Scholar 

  37. De Moor B. and Golub G. (1991). The restricted singular value decomposition: properties and applications. SIAM J. Matrix Anal. Appl. 12(3): 401–425

    Article  MATH  MathSciNet  Google Scholar 

  38. Vandewalle, J., De Moor, B.: On the use of the singular value decomposition in identification and signal processing. In: Proc. of the Workshop of the NATO Advanced Study Institute on Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms, pp. 321–361 (1988)

  39. Jung T.-P., Makeig S., McKeown M.J., Bell A.J., Lee T.-W. and Sejnowski T.J. (2001). Imaging brain dynamics using independent component analysis. Proc. IEEE 89(7): 1107–1122

    Article  Google Scholar 

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Authors and Affiliations

  1. University of Iowa, Iowa City, IA, USA

    Liangsuo Ma

  2. Hong Kong Baptist University, Kowloon, Hong Kong

    Ah Chung Tsoi

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  1. Liangsuo Ma
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  2. Ah Chung Tsoi
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Ma, L., Tsoi, A.C. A unified balanced approach to multichannel blind deconvolution. SIViP 1, 369–384 (2007). https://doi.org/10.1007/s11760-007-0030-7

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  • DOI: https://doi.org/10.1007/s11760-007-0030-7

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