Hidden Markov model-based speech enhancement using multivariate Laplace and Gaussian distributions

Ali Aroudi; Hadi Veisi; Hossein Sameti

Hidden Markov model-based speech enhancement using multivariate Laplace and Gaussian distributions

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Author(s): Ali Aroudi ¹ ; Hadi Veisi ² ; Hossein Sameti ¹
- Affiliations: 1: Department of Computer Engineering, Sharif University of Technology, Tehran, Islamic Republic of Iran;
  2: Faculty of New Sciences and Technologies (FNST), University of Tehran, Tehran, Islamic Republic of Iran
Source: Volume 9, Issue 2, April 2015, p. 177 – 185
DOI: 10.1049/iet-spr.2014.0032 , Print ISSN 1751-9675, Online ISSN 1751-9683

Received 23/01/2014, Accepted 25/08/2014, Revised 08/08/2014, Published 10/04/2015

In this paper, statistical speech enhancement using hidden Markov model (HMM) is studied and new techniques for applying non-Gaussian distributions are proposed. The superiority of using non-Gaussian distributions in online adaptive noise suppression algorithms has been proven; however, in this study, this approach is formulated in an HMM-based mean-square error estimator (MMSE) estimator in which a priori models are trained in an off-line manner. In addition, an analytical study of using different distributions other than autoregressive (AR) Gaussian distribution, such as Laplace, is presented in order to construct an accurate HMM as a priori model for discrete Fourier transform and discrete cosine transform feature vectors of speech signal. In the proposed framework, an HMM-based MMSE estimator bassed on Gaussian assumption using diagonal covariance matrix is provided rather than AR hypothesis which is employed in the conventional AR-HMM-based speech enhancement algorithm. Experimental evaluations of the proposed methods are done in the presence of four different noise types at various signal-to-noise ratio levels which demonstrate the superiority of the proposed methods in most conditions in comparison with AR-HMM.

References

1. 1)
  - 21. Gazor, S., Wei, Z.: ‘Speech enhancement employing Laplacian–Gaussian mixture’, IEEE Trans. Speech Audio Process., 2005, 13, (5), pp. 896–904 (doi: 10.1109/TSA.2005.851943).
2. 2)
  - 2. Laska, B.N.M., Bolic, M., Goubran, R.A.: ‘Particle filter enhancement of speech spectral amplitudes’, IEEE Trans. Audio Speech Lang. Process., 2010, 18, (8), pp. 2155–2167 (doi: 10.1109/TASL.2010.2042127).
3. 3)
  - 8. Lotter, T., Vary, P.: ‘Speech enhancement by map spectral amplitude estimation using a super-Gaussian speech model’, EURASIP J. Appl. Signal Process., 2005, 2005, pp. 1110–1126 (doi: 10.1155/ASP.2005.1110).
4. 4)
  - 12. Veisi, H., Sameti, H.: ‘Speech enhancement using hidden Markov models in Mel-frequency domain’, Speech Commun., 2013, 55, (2), pp. 205–220 (doi: 10.1016/j.specom.2012.08.005).
5. 5)
  - 9. Martin, R., Breithaupt, C.: ‘Speech enhancement in the DFT domain using Laplacian speech priors’. Int. Workshop on Acoustic Echo and Noise Control (IWAENC2003), Kyoto, Japan, September 2003.
6. 6)
  - 7. Erkelens, J.S., Jensen, J., Heusdens, R.: ‘Speech enhancement based on Rayleigh mixture modeling of speech spectral amplitude distributions’. European Signal Proc. Conf. (EUSIPCO), 2007.
7. 7)
  - 25. Kundu, A., Chatterjee, S., Sreenivas, T.V.: ‘Speech enhancement using intra-frame dependency in DCT domain’, in 16th European Signal Processing Conference (EUSIPCO 2008), Lausanne, Switzerland, August 25–29, 2008.
8. 8)
  - Y. Ephraim . A Bayesian estimation approach for speech enhancement using hidden Markov models. IEEE Trans. Signal Process. , 4 , 725 - 735
9. 9)
  - 6. Martin, R.: ‘Speech enhancement based on minimum mean-square error estimation and super Gaussian priors’, IEEE Trans. Speech Audio Process., 2005, 13, (5), pp. 845–856 (doi: 10.1109/TSA.2005.851927).
10. 10)
  - 11. Sameti, H., Deng, L.: ‘Nonstationary-state hidden Markov model representation of speech signals for speech enhancement’, Signal Process., 2002, 82, (2), pp. 205–227 (doi: 10.1016/S0165-1684(01)00179-7).
11. 11)
  - 28. Selesnick, I.W.: ‘The estimation of Laplace random vectors in additive white Gaussian noise’, IEEE Trans. Signal Process., 2008, 56, (8), pp. 3482–3496 (doi: 10.1109/TSP.2008.920488).
12. 12)
  - 3. Plourde, E., Champagne, B.: ‘Multidimensional STSA estimators for speech enhancement with correlated spectral components’, IEEE Trans. Signal Process., 2011, 59, (7), pp. 3013–3024 (doi: 10.1109/TSP.2011.2138697).
13. 13)
  - 32. Xin, Z., Jancovic, P., Ju, L., Kokuer, M.: ‘Speech signal enhancement based on MAP algorithm in the ICA space’, IEEE Trans. Signal Process., 2008, 56, (5), pp. 1812–1820 (doi: 10.1109/TSP.2007.910555).
14. 14)
  - S. Gazor , G. Zhang . Speech probability distribution. IEEE Signal Process. Lett. , 7 , 204 - 207
15. 15)
  - 13. Aroudi, A., Veisi, H., Sameti, H.: ‘Speech enhancement based on hidden Markov model with discrete cosine transform coefficients using Laplace and Gaussian distributions’. 2012 11th Int. Conf. on Information Science, Signal Processing and their Applications (ISSPA), 2012.
16. 16)
  - 30. (PESQ), P.E.o.S.Q.: ‘An objective method for end-to-end speech quality assessment of narrowband telephone networks and speech codecs’. ITU-T Recommendation, 2001, p. 862.
17. 17)
  - 20. Markel, J., Gray, A.Jr.: ‘On autocorrelation equations as applied to speech analysis’, IEEE Trans. Audio Electroacoust., 1973, 21, (2), pp. 69–79 (doi: 10.1109/TAU.1973.1162440).
18. 18)
  - 27. Wiener, N.: ‘Extrapolation, interpolation, and smoothing of stationary time series’ (The MIT Press, Cambridge, MA, 1949).
19. 19)
  - D.Y. Zhao , W.B. Kleijn . HMM-based gain modeling for enhancement of speech in noise. IEEE Trans. Audio Speech Lang. Process. , 3 , 882 - 892
20. 20)
  - 19. Biing-Hwang, J., Rabiner, L.: ‘Mixture autoregressive hidden Markov models for speech signals’, IEEE Trans. Acoust. Speech Signal Process., 1985, 33, (6), pp. 1404–1413 (doi: 10.1109/TASSP.1985.1164727).
21. 21)
  - 18. Bishop, C.M.: ‘Pattern recognition and machine learning (information science and statistics)’ (Springer-Verlag, Inc., New York, 2006).
22. 22)
  - 23. Eltoft, T., Taesu, K., Te-Won, L.: ‘On the multivariate Laplace distribution’, IEEE Signal Process. Lett., 2006, 13, (5), pp. 300–303 (doi: 10.1109/LSP.2006.870353).
23. 23)
  - L.R. Rabiner . A tutorial on hidden Markov models and selected applications in speech recognition. Proc. IEEE , 2 , 257 - 286
24. 24)
  - J.W. Shin , J.-H. Chang , N.S. Kim , S.K. Mitra . Statistical modeling of speech signals based on generalized gamma distribution. IEEE Signal Process. Lett. , 3 , 258 - 261
25. 25)
  - 10. Ephraim, Y.: ‘Statistical-model-based speech enhancement systems’, Proc. IEEE, 1992, 80, (10), pp. 1526–1555 (doi: 10.1109/5.168664).
26. 26)
  - 15. Black, A.W., Zen, H., Tokuda, K.: ‘Statistical parametric speech synthesis’. IEEE Int. Conf. on Acoustics, Speech and Signal Processing, 2007. ICASSP 2007, 2007.
27. 27)
  - 1. Chen, B., Loizou, P.C.: ‘A Laplacian-based MMSE estimator for speech enhancement’, Speech Commun., 2007, 49, (2), pp. 134–143 (doi: 10.1016/j.specom.2006.12.005).
28. 28)
  - Y. Ephraim , D. Malah . Speech enhancement using a minimum mean-square error short-time spectral amplitude estimator. IEEE Trans. Acoust. Speech Signal Process. , 6 , 1109 - 1121
29. 29)
  - 17. Dempster, A.P., Laird, N.M., Rubin, D.B.: ‘Maximum likelihood from incomplete data via the EM algorithm’, J. R. Stat. Soc. Ser. B (Methodol.), 1977, 39, (1), pp. 1–38.
30. 30)
  - 29. Manohar, K., Rao, P.: ‘Speech enhancement in nonstationary noise environments using noise properties’, Speech Commun., 2006, 48, (1), pp. 96–109 (doi: 10.1016/j.specom.2005.08.002).
31. 31)
  - Y. Hu , P.C. Loizou . Evaluation of objective quality measures for speech enhancement. IEEE Trans. Audio Speech Lang. Process. , 1 , 229 - 238
32. 32)
  - 22. Papoulis, A., Pillai, S.U.: ‘Probability, random variables and stochastic processes’ (Tata McGraw-Hill Education, 2002).
33. 33)
  - 16. Fazel, A., Chakrabartty, S.: ‘An overview of statistical pattern recognition techniques for speaker verification’, IEEE Circuits Syst. Mag., 2011, 11, (2), pp. 62–81 (doi: 10.1109/MCAS.2011.941080).

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Hidden Markov model-based speech enhancement using multivariate Laplace and Gaussian distributions

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