This document summarizes a research talk on statistical-model-based speech enhancement techniques that aim to reduce noise without generating musical noise artifacts. The talk outlines conventional enhancement methods like spectral subtraction and Wiener filtering that often cause musical noise. It then proposes a biased minimum mean-square error estimator that can achieve a musical-noise-free state by introducing a bias parameter. Analysis and experiments show this method can reduce noise while keeping the kurtosis ratio fixed at 1.0 to prevent musical noise, outperforming other techniques in terms of speech quality. A strong speech prior model is found to limit achieving musical-noise-free states, so the prior must be carefully selected.

1. Statistical-Model-Based Speech Enhancement
with Musical-Noise-Free Properties
Hiroshi Saruwatari
(The University of Tokyo, JAPAN)
IEEE DSP2015 Invited Talk

2. Outline
1. Research background
2. What is musical-noise-free?
3. Conventional statistical-model-based
speech enhancement
4. Proposed method and analysis
5. Experimental evaluation
6. Conclusion
2

3. Research Background and Goal
 Single-channel speech enhancement
 Spectral subtraction (SS) [Boll, 1979], Wiener Filtering,
Bayesian minimum mean-square error short-time
spectral amplitude (MMSE-STSA) estimator [Ephraim,
1984], MAP estimator [Lotter, 2005], etc.
 Harmful distortion owing to musical noise generation
 Musical-noise-free speech enhancement
[Miyazaki, Saruwatari et al., IEEE Trans. ASLP 2012]
 Noise reduction without any musical noise
 We have found that SS (maximum-likelihood amplitude
estimator) has musical-noise-free state.
 Whether or not Generalized Bayesian MMSE-STSA
estimator has musical-noise-free state?
3

4. Relation between Musical Noise and Kurtosis
4
Proportional relation
between human perception
(musical noise score) and
log kurtosis ratio
[Saruwatari, 2008]

5. What is Musical-Noise-Free?
5

6. Musical-Noise-Free Speech Enhancement
 Iterative noise reduction procedure with musical-noise-
free condition [Miyazaki, Saruwatari, et al., IEEE Trans. ASLP 2012]
6
…

7. MOSIE (generalized MMSE-STSA) Estimator
7
Statistical speech amplitude estimator with parametric
speech prior [Breithaupt, et al., IEEE Trans. 2011]

8. How to Generate Musical-Noise-Free State?
8
Unfortunately we cannot find any
musical-noise-free states in the
conventional MOSIE estimator.
No intersection!
Forgetting factor a
is increasing

9. Analysis Strategy
9

10. Calculation of Moment for Biased MOSIE (1/4)
10
1. Derivation of p.d.f.

11. Calculation of Moment for Biased MOSIE (2/4)
11
2. Calculation of moment for

12. Calculation of Moment for Biased MOSIE (3/4)
12
3. Moment-cumulant transformation for
4. Cumulant of noise power spectrum

13. Calculation of Moment for Biased MOSIE (4/4)
13
5. Cumulant-moment transformation for
m1 is used for NRR, and m2 and m4 are used for kurtosis,
which are functions of value of bias e.

14. Calculation of Moment for Biased MOSIE (4/4)
14
Bias e large

15. Experiment 1: Existence of Musical-Noise-Free
15
Noise White Gaussian noise in 0-dB SNR
Speech prior Gaussian model (r = 1)
Forgetting factor in DD 0.98
Noise PSD estimation Minimum Statistics Method [Martin, 1994]
Theoretical analysis Experimental results
Bias e = 0
To introduce bias ε, we find musical-noise-free state in
statistical-model-based estimator.
e large

16. Experiment 2: Existence of Musical-Noise-Free
16
Noise White Gaussian noise in 0-dB SNR
Speech prior Super Gaussian model (r = 0.5)
Forgetting factor in DD 0.98
Noise PSD estimation Minimum Statistics Method [Martin, 1994]
Theoretical analysis Experimental results
Bias e = 0
Strong speech prior (small ρ) gives almost no musical-
noise-free state in real processing.
e large

17. Experiment 3: Comparison with Other Methods
17
Speech 10 utterances
Noise White Gaussian noise in 0-dB SNR
Speech prior Super Gaussian model (r = 0.5, b = 0.001)
Forgetting factor in DD 0.98
Noise PSD estimation Minimum Statistics Method [Martin, 1994]
Target NRR 16 dB

18. Experiment 3: Comparison with Other Methods
18
Speech 10 utterances
Noise White Gaussian noise in 0-dB SNR
Speech prior Super Gaussian model (r = 0.5, b = 0.001)
Forgetting factor in DD 0.98
Noise PSD estimation Minimum Statistics Method [Martin, 1994]
Target NRR 16 dB
Large musical
noise methods
No musical noise methods

19. Experiment 3: Comparison with Other Methods
19
Speech 10 utterances
Noise White Gaussian noise in 0-dB SNR
Speech prior Super Gaussian model (r = 0.5, b = 0.001)
Forgetting factor in DD 0.98
Noise PSD estimation Minimum Statistics Method [Martin, 1994]
Target NRR 16 dB
Lowest
speech
distortion
Large musical
noise methods
No musical noise methods
Richer speech prior

20. Conclusion
 To introduce bias ε, we find musical-noise-free
state in Bayesian estimator.
 Proposed biased MOSIE estimator can achieve
better cepstral distortion whereas its kurtosis ratio
is perfectly fixed to 1.0.
 Strong speech prior (small ρ) gives almost no
musical-noise-free state. So we should carefully
select the appropriate prior to maintain the qualities
of both speech and remaining noise.
20
Thank you for your attention!