ECE Dept, ASE BLR 1

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

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ECE Dept, ASE BLR 2

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. Conclusion5/19/2014

ECE Dept, ASE BLR 3

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

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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

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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

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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)

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White Noise

• Impulse autocorrelation function • Flat power spectrum(equal power in all

frequencies)

a) Time-domain signal b) Autocorrelation c) PSD

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Wavelets

• Low frequency components gives the speech its identity

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Multiple Level Decomposition

• The decomposition process can be iterated, with successive approximations

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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 .

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(Roopali Goel et al.,2013)

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Simulation Results

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Noisy signal

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Denoised signal

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De-Noising noisy speech signal

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De-Noising sinusoidal signal

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Denoised signal

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Correlation b/w original and de-noised signal

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Correlation @ 0

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Conclusion

• Successfully able to remove AWGN

• A high correlation value above 98% at lag value of zero has been achieved

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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

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• 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

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• Relative error introduced when neglecting the cross terms is given by

• Relative error in terms of true SNR in frequency bin k

Algorithm(Contd…)

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• 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…)

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•New gain function with out assuming cross terms to be equal to zero is

• Using cosine rule

Algorithm(Contd…)

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•Dividing both numerator and denominator of cxd and cyd by

aD^2 we get

Where a posteriori SNR

a priori SNR

So

Algorithm(Contd…)

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• Instantaneous estimate of γ is

• To avoid rapid fluctuations smoothing of γ is done as follows

Algorithm(Contd…)

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• 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

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Smoothing of PSD

where smoothing parameter is

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Unbiased estimator of the noise power spectral density

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Simulation Result

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Screen Shot of Noisy and de-noised speech signal(babble)

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Screen Shot of Noisy and de-noised car noise signal

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Screen Shot of Noisy and de-noised AWGN signal

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Screen Shot of Noisy and de-noised when music is present as background noise

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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

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Future Scope

• De-noising the signal without assuming that the first 5 frames is only noise.

• To remove the background noise completely

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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

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