Literature Survey
Nonlinear Statistical Modelling of Speech

S. Patil, J. Picone
IES, CAVS
Mississippi State University, 
Starkville, MS, USA
Email: patil, picone@cavs.msstate.edu

Abstract—Nonlinear Statistical modeling of speech has the potential to be a revolutionary step forward over existing Gaussian models. Until recently, nonlinear modeling has not been a viable approach due to limitations in computing and understanding of these models. Speech has been modeled by Hidden Markov Models (HMM), Support Vector Machines(SVMs) and Relevance Vector Machines (RVMs). But, above methods have limited performance in presence of noise. Nonlinear models like Lyapunov exponents, strange attractors, Particle filtering have shown some promise in nonlinear statistical modeling. 
This literature survey introduces current trends in nonlinear statistical modeling of speech and possibilities made available for performance enhancement by its usage in the future.
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References
[1]	Y. Mahgoub and R. Dansereau, "Voicing-State Classification of Co-Channel Speech Using Nonlinear State-Space Recosntruction," ICASSP 2005, pp I-409 - I-412, March 2005.
[2]	M. Bocko, O. Altun, D. Headlam, and E. Titlebaum, "An Expressive And Compact Representation Of Musical Sound," ICASSP 2004, pp. IV-249 - IV-252, May 2004.
[3]	S. Chakrabartty, Y. Deng, and G. Cauwengberghs, "Robust Speech Feature Extraction By Growth Transformation In Producing Kernel Hilbert Space," ICASSP 2004, pp. I-133 - I-136, May 2004.
[4]	R. Gemello, F. Mana, and R. Mori, "A Modified Ephraim-Malah Noise Suppression Rule For Automatic Speech Recognition," ICASSP 2004, pp. I-957 - I-960, May 2004.
[5]	M. Jachan, G. Matz, and F. Hlawatsch, "Time-Frequency Moving-Average Processes: Principles And Cepstral Methods For Parameter Estimation,"  ICASSP 2004, pp. II- 757 - II-760, May 2004.
[6]	A. Lindgren, M. Johnson and R. Povinelli, "Speech Recognition Using Reconstructed Phase Space Features," ICASSP 2003, pp. I-60 - I-63, April 2003.
[7]	Y. Shi and E. Chang, "Spectrogram-Based Formant Tracking Via Particle Filters," ICASSP 2003, pp. I-168 - I-171, April 2003.
[8]	P. Spmervuo, "Experiments With Linear And Nonlinear Feature  Transformations In HMM Based Phone Recognition," ICASSP 2003, pp I-52 - I-55, April 2003.  
[9]	M. Omar and M. Johnson, "Approximately Independent Factors Of Speech Using Nonlinear Symplectic Transformation," IEEE transactions of speech and audio processing, vol 11, no. 6, pp 660-671, November 2003.
[10]	N. Kim, "Statistical Linear Approximation For Environment Compensation," IEEE signal processing letters, vol 5, no. 1, pp 8-10, January 1998.
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