1. Speech Enhancement Summer 2009
Pham Van Tuan
Electronic & Telecommunication Engineering
Danang University of Technology

2. ACKNOWLEDGMENT
1. Signal Processing & Speech Communication Institute, Graz University of Technology, Austria
Speech Communication 1,2
2. Dept. E.E./ESAT, K.U.Leuven
Noise Reduction, Marc Moonen/Ann Spriet
3. Peter Vary, Digital Speech Transmission, 2008
4. Tuan V. Pham, Wavelet Analysis For Robust Speech Processing and Applications, 2008

3. Introduction Aims: Noise Types:
Improvements in the intelligibility of speech to human listeners.
Improvement in the quality of speech that make it more acceptable to human listeners.
Modifications to the speech that lead to improved performance of automatic speech or speaker recognition systems.
Modifications to the speech so that it may be encoded more effectively for storage or transmission.
Noise Types:
Additive acoustic noise
Acoustic reverberation
Convolutive channel effects
Electrical interference
Codec distortion

4. General Scheme
The signal is firstly transformed into other domains to get a better presentation of the speech signal
The noise level is estimated by noise estimation
The noise component is removed out of the noisy speech signal by the gain function
Based on different linear estimators and non-linear estimators, a gain function will be designed.

5. Noise Estimation
Based on different linear estimators and non-linear estimators, a gain function will be designed
The most difficult parts in the noise reduction algorithms
Especially for non-stationary and non-white noise (whose characteristics change over time & over various frequency bands)
Single-channel noise reduction methods can be divided :
• Exploiting the periodicity of voiced speech.
• Auditory model based systems.
• Optimal linear estimators.
• Statistical model based systems using optimal non-linear estimators.
Due to the spectral overlap between speech and noise signals, the denoised speech signals obtained from single- channel methods exhibit more speech distortion
However, this method shows low cost and small size

6. ? Additive Noise Model Microphone signal is
Goal: Estimate s[k] based on y[k]
Applications: SE in conferencing, handsfree telephony, hearing aids, digital audio restoration, speech recognition, speech-based technology
Will consider speech applications: s[k] = speech signal
Can be stationary, non-stationary, narrowband, and broadband noise. Interference speakers is also considered.
desired signal
estimate
noise signal(s) ?
y[k]
desired signal
contribution
noise
contribution

7. Additive Noise Model
Strictly speaking: the estimation of statistical quantities via time averaging is only admissible when the signal is stationary and ergodic.
Signal chopped into `frames’ (e.g msec), for each frame i a frequency domain representation is
where the spectral components are short-time spectra of time domain signal frames (obtained from windowing technique using window w )
However, speech signal is an on/off (time-varying) signal, hence some frames have speech +noise, some frames have noise only,
A speech detection algorithm or Voice Activity Detection (VAD) is needed to distinguish between these 2 types of frames (based on statistical features) .

8. SE in DFT domain

9. Observation
Magnitude squared DFT coefs. of noisy, voiced speech sound and the estimated noise power spectral density (PSD) of the noisy speech.

10. Estimation Definition: () = average amplitude of noise spectrum
Assumption: noise characteristics change slowly, hence estimate () by (long-time) averaging over (M) noise-only frames
Estimate clean speech spectrum Si(), using Gain function Gi() of corrupted speech spectrum Yi() + estimated ():

11. Gain functions = most frequently used in practice
Magnitude Subtraction
Spectral Subtraction
Wiener Estimation
Maximum Likelihood
Non-linear Estimation
Ephraim-Malah Suppr. Rule
= most frequently used in practice

12. Spectral Subtraction Magnitude Subtraction Signal model:
Estimation of clean speech spectrum:
PS: half-wave rectification

13. Spectral Subtraction Power Spectral Subtraction Signal model:
Estimation of clean speech spectrum:
PS: half-wave rectification

14. Wiener Filter
Wiener Estimation
Goal: find linear filter Gi() such that MSE
is minimized
Solution: ( how ?)
Assume speech s[k] and noise n[k] are uncorrelated, then...
PS: half-wave rectification (as done so far)
<- cross-correlation in i-th frame
<- auto-correlation in i-th frame

15. Generalized Formula
Generalized magnitude squared spectral gain function
Practical heuristic form of spectral subtraction rule:

16. Suppressing Behaviors

17. Interpretation
Power Spectral Subtraction method is interpreted as a time- variant filter with magnitude frequency response:
The short-time energy spectrum |Yi()|2 of noisy speech signal is calculated directly. The noise level ()2 is estimated by averaging over many non-speech frames where the background noise is assumed to be stationary.
Negative values resulting from spectral subtraction are replaced by zero. This results into “musical noise”: a succession of randomly spaced spectral peaks emerges in the frequency bands -> the residual noise which is composed of narrow-band components located at random frequencies that turn on and off randomly in each short-time frame

18. magnitude subtraction

19. Solutions Flooring factor Over-subtraction factor
SNR-dependent subtraction factor
Averaging estimated noise level over K frames
Reduce noise variance at each frequency: apply a simple recursive first-order low-pass filter (using smoothing coef p controlling bandwidth & time constant of the LP filter)

20. Solutions
Solutions?
Magnitude averaging: replace Yi() in calculation of Gi() by a local average over frames
EMSR (p7)
augment Gi() with soft-decision VAD:
Gi()  P(H1 | Yi()). Gi() …
instantaneous
average
probability that speech is present, given observation

21. MMSE Estimation Ephraim-Malah Suppression Rule (EMSR) with:
modified Bessel functions
previous frame

22. Wavelet Denoising Additive noise model in Wavelet domain:
Hard-Thresholding
Soft-Thresholding
Shrinking

23. Hard Thresholding

24. Soft Thresholding

25. Optimal Shrinking

26. Noise Reduction for ASR

30. Short-time Stationary Processes
Strictly speaking: the estimation of statistical quantities via time averaging is only admissible when the signal is stationary and ergodic.

31. Short-time Stationary Processes

32. Power Spectral Density