Underdetermined Blind Mixing Matrix Estimation Using STWP Analysis for Speech Source Signals

ABSTRACT

Wavelet packets decompose signals in to broader components using linear spectral bisecting. Mixing matrix is the key issue in the Blind Source Separation (BSS) literature especially in under-determined cases. In this paper, we propose a simple and novel method in Short Time Wavelet Packet (STWP) analysis to estimate blindly the mixing matrix of speech signals from noise free linear mixtures in over-complete cases. In this paper, the Laplacian model is considered in short time-wavelet packets and is applied to each histogram of packets. Expectation Maximization (EM) algorithm is used to train the model and calculate the model parameters. In our simulations, comparison with the other recent results will be computed and it is shown that our results are better than others. It is shown that complexity of computation of model is decreased and consequently the speed of convergence is increased.

Wavelet packets decompose signals in to broader components using linear spectral bisecting. Mixing matrix is the key issue in the Blind Source Separation (BSS) literature especially in under-determined cases. In this paper, we propose a simple and novel method in Short Time Wavelet Packet (STWP) analysis to estimate blindly the mixing matrix of speech signals from noise free linear mixtures in over-complete cases. In this paper, the Laplacian model is considered in short time-wavelet packets and is applied to each histogram of packets. Expectation Maximization (EM) algorithm is used to train the model and calculate the model parameters. In our simulations, comparison with the other recent results will be computed and it is shown that our results are better than others. It is shown that complexity of computation of model is decreased and consequently the speed of convergence is increased.

KEYWORDS

ICA, CWT, DWT, BSS, WPD, Laplacian Model, Expectation Maximization, Wavelet Packets, Short Time analysis, Over-complete, Blind Source Separation, Speech Processing

ICA, CWT, DWT, BSS, WPD, Laplacian Model, Expectation Maximization, Wavelet Packets, Short Time analysis, Over-complete, Blind Source Separation, Speech Processing

Cite this paper

nullB. Tazehkand and M. Tinati, "Underdetermined Blind Mixing Matrix Estimation Using STWP Analysis for Speech Source Signals,"*Wireless Sensor Network*, Vol. 2 No. 11, 2010, pp. 854-860. doi: 10.4236/wsn.2010.211103.

nullB. Tazehkand and M. Tinati, "Underdetermined Blind Mixing Matrix Estimation Using STWP Analysis for Speech Source Signals,"

References

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[2] B. Karlsen, H. B. Sorensen, J. Larsen and K. B. Jackobsen, “Independent Component Analysis for Clutter Reduction in Ground Penetrating Radar Data,” Proceedings of the SPIE, AeroSense 2002, Vol. 4742, SPIE, 2002, pp. 378-389.

[3] J.-F. Cardoso, “Blind Signal Separation: Statistical Principles,” Proceedings of the IEEE, Vol. 86, No. 10, 1998, pp. 2009-2025.

[4] P. Comon, “Independent Component Analysis—A New Concept?” Signal Processing, Vol. 36, No. 3, 1994. pp. 287-314.

[5] T. W. Lee, “Independent Component Analysis: Theory and Applications,” MA: Kluwer, Boston, 1998.

[6] J. Anemüller and B. Kollmeier, “Adaptive Separation of Acoustic Sources for Anechoic Conditions: A Constrained Frequency Domain Approach,” Speech Communication, Vol. 39, No. 1-2, January 2003, pp. 79-95.

[7] Y. Li, A. Cichocki and S. I. Amari, “Sparce Component Analysis for Blind Source Separation with Less Sensors than Sources,” 4th International Symposium on ICA and BSS (ICA2003), Nara, Japan, April 2003, pp. 89-94.

[8] Z. Shi, H. Tang and Y. Tang, “Blind Source Separation of More Sources than Mixtures Using Sparse Mixture Models,” Pattern Recognition Letter, Vol. 26, No. 16, December 2005, pp. 2491-2499.

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[10] O. Yilmaz and S. rickard, “Blind Separation of Speech Mixtures via Time-Frequency Masking,” IEEE Transactions on Signal Processing, Vol. 52, No. 7, 2004, pp. 1830-1847.

[11] P. Bofill and M. Zibulevsky, “Underdetermined Blind Source Separation Using Sparce Representation Networks,” Signal Processing, Vol. 81, No. 11, November 2001, pp. 2353-2362.

[12] L. Vielva, D. Erdogmus and J. C. Principe, “Underdetermined Blind Source Separation Using a Probabilistic Source Sparsity Model,” International Conference on ICA and Signal Separation, (ICA 2001), San Diego, Calif, USA, December 2001, pp. 675-679.

[13] M. Lewicki and T. J. Sejnowski, “Learning over Complete Representations Networks,” Neural Computer, Vol. 12, No. 2, 2000, pp. 337-365.

[14] M. A. Tinati and B. Mozaffari, “Comparison of Time-Frequency and Time-Scale Analysis of Speech Signals Using STFT and DWT,” WSEAS Transaction on Signal Processing, Vol. 1, No. 1, October 2005, pp. 11-16.

[15] B. Mozaffari and M. A. Tinati, “Blind Source Separation of Speech Sources in Wavelet Packet Domains Using Laplacian Mixture Model Expectation Maximization Estimation in Over-complete- Cases,” Journal of Statistical Mechanics: Theory and Experiments An IOP and SISSA Journal, 2007, pp. 1-31.

[16] M. A. Tinati and B. Mozaffari, “A Novel Method to Estimate Mixing Matrix under Over-complete Cases in Wavelet Packet Domain,” ICCCE08, Kuala Lumpur, 2008, pp. 493-496.

[17] C. S. Burrus, R. A. Gopinath and H. Guo, “Introduction to Wavelets and Wavelet Transforms, a Primer,” Prentice Hall, New Jersey, 1998.

[18] I. Daubechies, “Ten Lectures on Wavelets,” CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics, Vol. 61, 1992.

[19] S. Mallat, “A Wavelet Tour of Signal Processing,” 2nd Edition, Academic Press, Elsevier, 1999.

[20] S. G. Mallat, “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11, No. 7, July 1989, pp. 674-693.

[21] A. Grossman, R. Kronland-Martinent and J. Morlet, “Reading and Understanding Continuous Wavelet Transform,” Proceedings of International Conference on Wavelets, Time-Frequency Methods and Phase Spaces, Marselle, France, 14-18 December, 1987, p. 2.

[22] F. J. Theis, C. G. Puntonet and E. W. Lang, “A Histogram Based Overcomplete ICA Algorithm,” In Proceedings of ICA2003, Nara, Japan, 2003, pp. 1071-1076.

[23] A. K. Barros, H. Kawahara, A. Cichocki, S. Kojita, T. Rutkowski, M. Kawamoto and N. Ohnishi, “Enhancement of Speech Signal Embedded in Noisy Environment Using Two Microphones,” Proceedings of the Second International Workshop on ICA and BSS, ICA2000, Helsinki, Finland, 19-22 June 2000, pp. 423-428.

[24] M. A. Tinati and B. Mozaffari, “A Novel Method for Noise Cancellation of Speech Signals Using Wavelet Packets,” The 7th International Conference on Advanced Communication Technology, ICACT2005, Vol. 1, 2005, pp. 35-38.

[25] M. Zibulevsky, P. Kisilev, Y. Y. Zeevi and B. A. Pearlmutter, “Blind Source Separation via Multimode Sparse Representation Networks,” Advances in Neural Information Processing Systems, Vol. 14, 2002, pp. 1049-1056.

[26] N. Mitianoudis and T. Stathaki, “Overcomplete Source Separation Using Laplacian Mixture Models,” IEEE Signal Processing Letters, Vol. 18, No. 4, 2004. pp. 277-280.

[27] S. G. Kim, “Underdetermind Blind Source Separation Based on Subspace Representation,” IEEE Transactions on Signal Processing, Vol. 57, No. 7, July 2009, pp. 2604 -2614.

[1] M. McKeown, L. K. Hansen and T. J. Sejnowski, “Independent Component Analysis for fMRI: What is Signal and What is Noise?” Current Opinion in Neurobiology, Vol. 13, No. 5, 2003, pp. 620-629.

[2] B. Karlsen, H. B. Sorensen, J. Larsen and K. B. Jackobsen, “Independent Component Analysis for Clutter Reduction in Ground Penetrating Radar Data,” Proceedings of the SPIE, AeroSense 2002, Vol. 4742, SPIE, 2002, pp. 378-389.

[3] J.-F. Cardoso, “Blind Signal Separation: Statistical Principles,” Proceedings of the IEEE, Vol. 86, No. 10, 1998, pp. 2009-2025.

[4] P. Comon, “Independent Component Analysis—A New Concept?” Signal Processing, Vol. 36, No. 3, 1994. pp. 287-314.

[5] T. W. Lee, “Independent Component Analysis: Theory and Applications,” MA: Kluwer, Boston, 1998.

[6] J. Anemüller and B. Kollmeier, “Adaptive Separation of Acoustic Sources for Anechoic Conditions: A Constrained Frequency Domain Approach,” Speech Communication, Vol. 39, No. 1-2, January 2003, pp. 79-95.

[7] Y. Li, A. Cichocki and S. I. Amari, “Sparce Component Analysis for Blind Source Separation with Less Sensors than Sources,” 4th International Symposium on ICA and BSS (ICA2003), Nara, Japan, April 2003, pp. 89-94.

[8] Z. Shi, H. Tang and Y. Tang, “Blind Source Separation of More Sources than Mixtures Using Sparse Mixture Models,” Pattern Recognition Letter, Vol. 26, No. 16, December 2005, pp. 2491-2499.

[9] S. rickard, R. balan and J. Rosca, “Blind Source Separation Based on Space-Time-Frequency Divercity,” IEEE Transactions on Signal Processing, Vol. 46, No. 11, November 1998, pp. 2888-2897.

[10] O. Yilmaz and S. rickard, “Blind Separation of Speech Mixtures via Time-Frequency Masking,” IEEE Transactions on Signal Processing, Vol. 52, No. 7, 2004, pp. 1830-1847.

[11] P. Bofill and M. Zibulevsky, “Underdetermined Blind Source Separation Using Sparce Representation Networks,” Signal Processing, Vol. 81, No. 11, November 2001, pp. 2353-2362.

[12] L. Vielva, D. Erdogmus and J. C. Principe, “Underdetermined Blind Source Separation Using a Probabilistic Source Sparsity Model,” International Conference on ICA and Signal Separation, (ICA 2001), San Diego, Calif, USA, December 2001, pp. 675-679.

[13] M. Lewicki and T. J. Sejnowski, “Learning over Complete Representations Networks,” Neural Computer, Vol. 12, No. 2, 2000, pp. 337-365.

[14] M. A. Tinati and B. Mozaffari, “Comparison of Time-Frequency and Time-Scale Analysis of Speech Signals Using STFT and DWT,” WSEAS Transaction on Signal Processing, Vol. 1, No. 1, October 2005, pp. 11-16.

[15] B. Mozaffari and M. A. Tinati, “Blind Source Separation of Speech Sources in Wavelet Packet Domains Using Laplacian Mixture Model Expectation Maximization Estimation in Over-complete- Cases,” Journal of Statistical Mechanics: Theory and Experiments An IOP and SISSA Journal, 2007, pp. 1-31.

[16] M. A. Tinati and B. Mozaffari, “A Novel Method to Estimate Mixing Matrix under Over-complete Cases in Wavelet Packet Domain,” ICCCE08, Kuala Lumpur, 2008, pp. 493-496.

[17] C. S. Burrus, R. A. Gopinath and H. Guo, “Introduction to Wavelets and Wavelet Transforms, a Primer,” Prentice Hall, New Jersey, 1998.

[18] I. Daubechies, “Ten Lectures on Wavelets,” CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics, Vol. 61, 1992.

[19] S. Mallat, “A Wavelet Tour of Signal Processing,” 2nd Edition, Academic Press, Elsevier, 1999.

[20] S. G. Mallat, “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11, No. 7, July 1989, pp. 674-693.

[21] A. Grossman, R. Kronland-Martinent and J. Morlet, “Reading and Understanding Continuous Wavelet Transform,” Proceedings of International Conference on Wavelets, Time-Frequency Methods and Phase Spaces, Marselle, France, 14-18 December, 1987, p. 2.

[22] F. J. Theis, C. G. Puntonet and E. W. Lang, “A Histogram Based Overcomplete ICA Algorithm,” In Proceedings of ICA2003, Nara, Japan, 2003, pp. 1071-1076.

[23] A. K. Barros, H. Kawahara, A. Cichocki, S. Kojita, T. Rutkowski, M. Kawamoto and N. Ohnishi, “Enhancement of Speech Signal Embedded in Noisy Environment Using Two Microphones,” Proceedings of the Second International Workshop on ICA and BSS, ICA2000, Helsinki, Finland, 19-22 June 2000, pp. 423-428.

[24] M. A. Tinati and B. Mozaffari, “A Novel Method for Noise Cancellation of Speech Signals Using Wavelet Packets,” The 7th International Conference on Advanced Communication Technology, ICACT2005, Vol. 1, 2005, pp. 35-38.

[25] M. Zibulevsky, P. Kisilev, Y. Y. Zeevi and B. A. Pearlmutter, “Blind Source Separation via Multimode Sparse Representation Networks,” Advances in Neural Information Processing Systems, Vol. 14, 2002, pp. 1049-1056.

[26] N. Mitianoudis and T. Stathaki, “Overcomplete Source Separation Using Laplacian Mixture Models,” IEEE Signal Processing Letters, Vol. 18, No. 4, 2004. pp. 277-280.

[27] S. G. Kim, “Underdetermind Blind Source Separation Based on Subspace Representation,” IEEE Transactions on Signal Processing, Vol. 57, No. 7, July 2009, pp. 2604 -2614.