A noise-estimation algorithm for highly non-stationary environments

1. A noise-estimation algorithm for highly non-stationary environments Sundarrajan Rangachari, Philipos C. Loizou Department of Electrical Engineering, University of Texas at Dallas, P.O. Box 830688, EC 33 Richardson, TX 75083-0688, USA Presenter: Shih-Hsiang(士翔) SPEECH COMMUNICATION Vol. 48(2), 2006

2. Reference • Doblinger, G., 1995. Computationally efficient speech enhancement by spectral minima tracking in subbands. Proc. Eurospeech 2, 1513–1516. • Hirsch, H., Ehrlicher, C., 1995. Noise estimation techniques for robust speech recognition. Proc. IEEE Internat. Conf. on Acoust. Speech Signal Process., 153–156. • Martin, R., 2001. Noise power spectral density estimation based on optimal smoothing and minimum statistics. IEEE Trans. Speech Audio Process. 9 (5), 504–512. • Cohen, I., 2002. Noise estimation by minima controlled recursive averaging for robust speech enhancement. IEEE Signal Process. Lett. 9 (1), 12–15. • Hu, Y., Loizou, P., 2004. Speech enhancement based on wavelet thresholding the multitaper spectrum. IEEE Trans. Speech Audio Process. 12 (1), 59–67.

3. Introduction • In most speech-enhancement algorithms, it is make assumed that an estimate of the noise spectrum is available • It is critical for the performance of speech-enhancement algorithms • The noise estimate can have a major impact on the quality of the enhanced signal • If the noise estimate is too low, annoying residual noise will be audible • If the noise estimate is too high, speech will be distorted • The simplest approach is to estimate and update the noise spectrum during the silent segments of the signal • Using a voice activity detection (VAD) algorithm • It only work satisfactorily in stationary noise, not work well in more realistic environments (non-stationary noise) • Hence there is a need to update the noise spectrum continuously over time

4. Proposed noise-estimation algorithmsCompute smooth speech power spectrum Let the noisy speech signal in the time domain be denoted as Noisy speech Clean speech Additive noise The smoothed power spectrum of noisy speech is computed using the following first-order recursive equation Smoothing constant Frame index Frequency index Smooth power spectrum

5. Proposed noise-estimation algorithmsTracking the minimum of noisy speech Local minimum of the noisy speech power spectrum β and γ are constants which are determined experimentally The look ahead factor β controls the adaptation time of the local minimum

6. Proposed noise-estimation algorithmsTracking the minimum of noisy speech Plot of noisy speech power spectrum and local minimum using (3) for a speech degraded by babble noise at 5 dB SNR at frequency bin k=5

7. Proposed noise-estimation algorithmsSpeech-presence probability Let the ratio of noisy speech power spectrum and its local minimum be defined as The power spectrum of noisy speech will be nearly equal to its local minimum when speech is absent The speech-presence probability, P(λ,k), is updated using the following first-order recursion Smoothing constant The above recursion implicitly exploits the correlation for speech presence in adjacent frames

8. Proposed noise-estimation algorithmsSpeech-presence probability Top panel: Plot of estimated speech-presence probability based on the ratio Sr(λ,k) Bottom panel: spectrogram of the clean signal.

9. Proposed noise-estimation algorithmsComputing frequency-dependent smoothing constants Using the speech-presence probability estimate, we compute the time-frequency dependent smoothing factor as follows constant Note that αs(λ ,k) take values in the range of αd ≤ αs(λ ,k) ≤ 1 Finally, the noise spectrum estimate is updated as

10. Proposed noise-estimation algorithms Plot of true noise spectrum and the estimated noise spectrum using our proposed method for a speech degraded by babble noise at 5 dB SNR and single frequency f = 250 Hz.

11. Comparison with existing algorithmsMinimum statistics (MS)(Martin, 2001) • Minimum statistics (MS) (Martin, 2001) the power spectral densities of the noise signal Equivalent degrees of freedom

12. Comparison with existing algorithmsMinimum statistics (MS)(Martin, 2001) Comparison between the noise spectrum estimated using the proposed algorithm (thick line) and Martins (Martin, 2001) (dashed line) algorithm for a sentence corrupted by car noise (t < 1.8 s) followed by a sentence corrupted by multi-talker babble (t > 1.8 s).

13. Comparison with existing algorithmsContinuous minima tracking (Doblinger, 1995) • Continuous minima tracking (Doblinger, 1995) Drawback: the noise estimate increases whenever the noisy speech power increases

14. Comparison with existing algorithmsContinuous minima tracking (Doblinger, 1995) Top panel: Plot of true noise spectrum and estimated noise spectrum using the proposed method Bottom panel: Plot of true noise spectrum and estimated noise spectrum using (Doblinger, 1995) Arrows indicate regions where noise is overestimated.

15. Comparison with existing algorithmsWeighted average technique (Hirsch et al., 1995) • Weighted average technique (Hirsch and Ehrliche , 1995) It fails when there is a sudden increase in noise level. This will result in a situation where the noisy speech spectrum will never be smaller than the threshold, since the threshold is based on the past noise estimates already very low. Thus, the noise estimate will not be updated if the noise power remains at that high level spectral magnitude l-th frame estimate noise magnitude i-th subband

16. Comparison with existing algorithmsWeighted average technique (Hirsch et al., 1995) Comparison of estimated noise spectrum (f = 500 Hz) of proposed method (dashed line) with that of Hirsch and Ehrlicher (1995) (solid line) for a noisy speech of SNR 20 dB (t < 1.8 s) followed by a noisy speech of SNR 5 dB (t > 1.8 s).

17. Comparison with existing algorithmsMinima controlled Recursive Averaging (Cohen,2002) • Minima controlled Recursive Averaging (MRCA) (Cohen,2002) Given two hypotheses l-th frame speech absence speech presence k-th subband Let λd(k,l)=E[|D(k,l)|2] denote the variance of the noise in the k-th band speech absence speech presence Smoothing constant Let p’(k,l)=p(H’1(k,l)|Y(k,l))denote the conditional signal presence probability where

18. Comparison with existing algorithmsMinima controlled Recursive Averaging (Cohen,2002) Let the local energy of the noisy speech be obtained by smoothing the magnitude squared of its STFT in time and frequency. In frequency, use a window function b whose length is 2w+1 In time, the smoothing is performed by a first order recursive averaging, given by Track the minimum of the local energy Speech presence is determined by the ratio between the local energy of the noisy speech and its minimum within a specified time window The conditional signal presence probability calculated as follow

19. Comparison with existing algorithmsMinima controlled Recursive Averaging (Cohen,2002) • The local minimum in (Cohen, 2002) was found by tracking the minimum of noisy speech over a search window spanning L frames, this has some drawbacks: • The minimum is sensitive to outliers • The minima tracking may lag by as many as 2L frames • In this paper • The estimate of the noise spectrum in the proposed method is not influenced by the minimum-search window • the threshold used in our method for identifying speech presence /absence regions is frequency dependent while that of Cohen (2002) is fixed for all frequencies

20. Experimental • Combined with a Wiener-type speech-enhancement algorithm (Hu and Loizou, 2004) • Estimate the spectral gain function where C(λ,k) is the estimated clean speech spectrum compute as follow where v=0.001 is a small positive number μmax is the maximum allowable value of μ ,which was set to 10 μ0=(1+4 μmax)/5 s=25/(μmax-1)

21. Experimental (cont.) • Obtain the enhanced spectrum • Other parameters αd=0.85, αp=0.2, β=0.8, γ=0.998, η=0.7 where X(λ,k) is the enhanced spectrum where LF and MF are the bins corresponding to 1 and 3 kHz, and Fs is the sampling frequency

22. Experimental ResultSubjective evaluation • Using formal listening tests • Single noise Sentences were degraded by either multi-talker babble noise or factory noise • Triplet noise Three different noise types (multi-talker babble, factory noise, and white noise) appear in proper order without any pauses in the middle • The listeners were asked to select from the pair of stimuli presented the sentence which was more natural, easier to listen and free of artifacts • A preference score of 100% would indicate that listeners preferred the proposed method over the other methods all the time

23. Experimental ResultSubjective evaluation due to the fact that proposed noise-estimation algorithm adapts quickly to the highly non-stationary environments

24. Experimental ResultObjective evaluation • Mean squared error between the true noise spectrum and the estimated noise spectrum • Log-likelihood ratio (LLR) measure estimated noise power spectrum total frame number true noise power spectrum linear prediction coefficient vector of the enhanced speech frame The LLR is a spectral distance measure which mainly models the mismatch between the formants of the original and enhanced signals autocorrelation matrix of the original (clean) speech frame linear prediction coefficient vector of the original (clean) speech frame

25. Experimental ResultObjective evaluation • Segmental SNR the set of frames that contain speech

26. Experimental ResultObjective evaluation (MSE) The MSE results are not consistent with the preference outcomes, in that lower MSE values did not suggest better preference. This indicates that the MSE measure might not be a reliable measure for assessing performance of noise-estimation algorithms. 1. this measure is sensitive to outlier values 2. it treats noise overestimation and noise underestimation errors the same

27. Experimental ResultObjective evaluation (LLR and SNR) The segmental SNR values and the LLR values shown in Table 3 were found to be more consistent with the subjective evaluation results

28. Experimental Result Panel A – Clean Speech Panel C – Martins (2001) Panel E - Proposed method Panel B – Noisy Speech Panel D – Cohen (2003)

29. Conclusions • The noise estimate was updated continuously in every frame using time–frequency smoothing factors calculated based on speech-presence probability in each frequency bin of the noisy speech spectrum • The speech-presence probability was estimated using the ratio of noisy speech power spectrum to its local minimum • The update of noise estimate was faster for very rapidly varying non-stationary noise environments