Geometric Approach to Spectral Substraction

A GEOMETRIC APPROACH TO SPECTRAL
SUBSTRACTION AND ADDITIVE WHITE GAUSSIAN
NOISE REMOVAL USING WAVELETS
P. S. Manasa :BL.EN.U4ECE10138
Keerthi Thallam :BL.EN.U4ECE10190
Guided by
Dr. Shikha Tripathi
Presented by
5/19/2014 ECE Dept, ASE BLR 1

Contents
• Introduction
• Outline of mid-semester presentation
• White noise
• Wavelet theory
• De-noising using wavelet theory
1. Algorithm
2. Simulation results
3. Conclusion
• A Geometric approach to Spectral Subtraction
1. Algorithm
2. Simulation results
3. Conclusion

Introduction
• Speech enhancement (i.e removal noise from speech) is
necessary to improve user perception
• Noise degrades the quality of the information signal
• De-Noising plays a major role in communication
• Different de-noising techniques can be employed for different
noises

Transient noise reduction using diffusion
filters
Estimation power spectral density (PSD) of the transient noise
by employing a NL neighborhood filter
• Modeling speech signal as an autoregressive (AR) process in
short-time frames
• Decorrelating the noisy measurement y(n) in each time frame
using the AR parameters
• Find Fourier transform coefficients in each frame and find the
PSD

Transient noise reduction using diffusion
filters (Contd…)
• Modeling transient noise d(n) as d(n) = h(n) ∗ (b(n)v(n))
• Kernel to find out frames with and without transient noise

Methods Implemented
Method 1: Reduction of noise(AWGN) using
wavelets (Roopali Goel et al.,2013)
Method 2: Geometric approach to spectral
subtraction (Yang Lu et al.,2008)

White Noise
• Impulse autocorrelation function
• Flat power spectrum(equal power in all
frequencies)
a) Time-domain signal b) Autocorrelation c) PSD

Wavelets
• Low frequency components gives the speech
its identity

Multiple Level Decomposition
• The decomposition process can be iterated,
with successive approximations

De-Noising Using Wavelets
Algorithm
• Noisy signal should be decomposed into tree of high and low
frequency components.
• For any particular level of the decomposed signal (tree)
wavelet coefficients should be found out.
• Tree level should be selected such that it gives better
performance.
• Threshold should be fount out using ‘Birge-Massart’
algorithm
• Using the threshold value soft thresholding of the high
frequency components is done .
(Roopali Goel et al.,2013)

Simulation Results
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 10
4
-0.2
0
0.2
0.4
0.6
time
Amplitude
original signal
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 10
4
-0.2
-0.1
0
0.1
0.2
time
Amplitude
Noisy signal
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 10
4
-0.2
-0.1
0
0.1
0.2
time
Amplitude
Denoised signal
De-Noising noisy speech signal

De-Noising sinusoidal signal
0 500 1000 1500 2000 2500
-1
0
1
time
Amplitude
original signal
0 500 1000 1500 2000 2500
-2
0
2
time
Amplitude
Noisy signal
0 500 1000 1500 2000 2500
-2
0
2
time
Amplitude
Denoised signal

Correlation b/w original and de-noised
signal
-20 -15 -10 -5 0 5 10 15 20
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
coif 5
lag
samplecrosscorrelation
Correlation @ 0

Conclusion
• Successfully able to remove AWGN
• A high correlation value above 98% at lag
value of zero has been achieved

A geometric approach to spectral
subtraction (Yang Lu et al.,2008)
• Does not suffer from musical noise distortion
• Does not assume that the cross terms are zero
• Performs significantly better than the traditional spectral subtractive
algorithm
• Based on representing the noisy speech spectrum in the complex plane
as the sum of the clean signal and noise vectors

• let y(n) = x(n) + d(n)
Where y(n)= sampled noisy speech signal
x(n)= clean signal
d(n)= noise signal
•Taking the short-time Fourier transform of y(n)
Where N is the frame length in samples
• Short-term power spectrum of the noisy speech
Algorithm

• Relative error introduced when neglecting the cross terms is
given by
• Relative error in terms of true SNR in frequency bin k
Algorithm(Contd…)

• Equation of noisy speech signal in polar form
Representation of Noise spectrum in complex plane as the sum of clean
signal spectrum and noise spectrum
Algorithm(Contd…)

•New gain function with out assuming cross terms to be equal
to zero is
• Using cosine rule
Algorithm(Contd…)

•Dividing both numerator and denominator of cxd and cyd by
aD^2 we get
Where
a posteriori SNR
a priori SNR
So
Algorithm(Contd…)

• Instantaneous estimate of γ is
• To avoid rapid fluctuations smoothing of γ is done as follows
Algorithm(Contd…)

• Does not use a voice activity detector
• Tracks spectral minima in each frequency band
• Optimally smoothed power spectral density is estimated
• Develops an unbiased noise power spectral density estimator
Noise Power Spectral Density
Estimation

Smoothing of PSD
where smoothing parameter is

Unbiased estimator of the noise power
spectral density

Simulation Result
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 10
4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 10
4
-0.4
-0.2
0
0.2
0.4
Screen Shot of Noisy and de-noised speech signal(babble)

0 2 4 6 8 10 12 14
x 10
4
-1
-0.5
0
0.5
1
1.5
0 2 4 6 8 10 12 14
x 10
4
-1
-0.5
0
0.5
1
Screen Shot of Noisy and de-noised car noise signal

Screen Shot of Noisy and de-noised AWGN signal
0 0.5 1 1.5 2 2.5 3 3.5
x 10
5
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.5 1 1.5 2 2.5 3 3.5
x 10
5
-1
-0.5
0
0.5
1

0 0.5 1 1.5 2 2.5
x 10
5
-2
-1
0
1
2
0 0.5 1 1.5 2 2.5
x 10
5
-1
-0.5
0
0.5
1
Screen Shot of Noisy and de-noised when music is present as background noise

Conclusion
• Successfully able to reduce several types of
noise like babble, white , music , AWGN
• It shows better performance compared to that
of traditional spectral subtraction algorithms
• It can remove noise from low as well as high
SNR speech

Future Scope
• De-noising the signal without assuming that
the first 5 frames is only noise.
• To remove the background noise completely

References
• Roopali Goel, Ritesh Jain “Speech Signal Noise Reduction by Wavelets”
International Journal of Innovative Technology and Exploring Engineering
(IJITEE) ISSN: 2278-3075, Volume-2, Issue-4, March 2013
• Yang Lu, Philipos C. Loizou “A geometric approach to spectral subtraction”
Department of Electrical Engineering, University of Texas-Dallas, Richardson,
TX 75083-0688, United States 24 January 2008.
• Adrian E. Villanueva- Luna1, Alberto Jaramillo-Nuñez1, Daniel Sanchez-
Lucero1, Carlos M. Ortiz-Lima1,J. Gabriel Aguilar-Soto1, Aaron Flores-Gil2 and
Manuel May-Alarcon “Denoising audio signals” using matlab Instituto
Nacional de Astrofisica, Optica y Electronica (INAOE) Universidad Autonoma
del Carmen (UNACAR) Mexico.
• Martin R., 2001. Noise power spectral density estimation based on
optimal smoothing and minimum statistics. IEEE Trans. Speech
Audio Process. 9 (5), 504–512

Geometric Approach to Spectral Substraction

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