Best Speech Enhancement Estimator in the Frequency Domain

Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)


This chapter gives a fresh perspective on the best speech enhancement estimator in the frequency domain. We consider the general nonlinear case. In the first part, we deal with the single-channel scenario, where an example is studied with gamma distributions and a best quadratic estimator is derived. Then, in the second part, we focus on the multichannel scenario.


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  1. 1.
    J. Benesty, J. Chen, Y. Huang, and I. Cohen, Noise Reduction in Speech Processing. Berlin, Germany: Springer-Verlag, 2009.Google Scholar
  2. 2.
    P. Loizou, Speech Enhancement: Theory and Practice. Boca Raton, FL: CRC Press, 2007.Google Scholar
  3. 3.
    J. Benesty, J. Chen, and E. Habets, Speech Enhancement in the STFT Domain. Springer Briefs in Electrical and Computer Engineering, 2011.Google Scholar
  4. 4.
    N. A. Weiss, P. T. Holmes, and M. Hardy, A Course in Probability. Boston: Addison-Wesley, 2005.Google Scholar
  5. 5.
    R. Steyer, “Conditional expectations: an introduction to the concept and its applications in empirical sciences,” Methodika, vol. 2, issue 1, pp. 53–78, 1988.Google Scholar
  6. 6.
    S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Upper Saddle River, NJ: Prentice Hall PTR, 1993.Google Scholar
  7. 7.
    R. Martin, “Speech enhancement using MMSE short time spectral estimation with gamma distributed speech priors,” in Proc. IEEE ICASSP, 2002, pp. I-253–I-256.Google Scholar
  8. 8.
    R. C. Hendriks, J. S. Erkelens, J. Jensen, and R. Heusdens, “Minimum mean-square error amplitude estimators for speech enhancement under the generalized gamma distribution,” in Proc. IWAENC, 2006.Google Scholar
  9. 9.
    J. S. Erkelens, R. C. Hendriks, R. Heusdens, and J. Jensen, “Minimum mean-square error estimation of discrete Fourier coefficients with generalized gamma priors,” IEEE Trans. Audio, Speech, Language Process., vol. 15, pp. 1741–1752, Aug. 2007.Google Scholar
  10. 10.
    B. Fodor and T. Fingscheidt, “MMSE speech enhancement under speech presence uncertainty assuming (generalized) gamma speech priors throughout,” in Proc. IEEE ICASSP, 2012, pp. 4033–4036.Google Scholar
  11. 11.
    J. Benesty, J. Chen, and Y. Huang, Microphone Array Signal Processing. Berlin, Germany: Springer-Verlag, 2008.Google Scholar

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© The Author(s) 2018

Authors and Affiliations

  1. 1.INRS EMT, Suite 6900University of QuebecMontrealCanada

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