Speech Enhancement Using Compressive Sensing
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The document proposes a method for speech enhancement using compressive sensing. It involves compressing a speech signal using a measurement matrix at the transmitter and then reconstructing it at the receiver from fewer samples than the Nyquist rate. The method takes a noisy speech signal, applies a discrete cosine transform, uses thresholding to eliminate small coefficients, and then reconstructs the signal using l1-minimization. Simulation results show the method can compress signals by 40% with low error rates and reconstruct the signal without losing important information, increasing data rates. Future work could involve testing different transformations and designing an optimal measurement matrix for speech signals.
![International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1125
Speech Enhancement using Compressive Sensing
K.Kiruthiga1, J.Indra2
1PG Scholar,Dept. Of EIE, Kongu Engineering College, Tamilnadu,India
2Assistant Professor (SLG),Dept. Of EIE, Kongu Engineering College, Tamilnadu, India
---------------------------------------------------------------------***-----------------------------------------------------------------
Abstract - Speech enhancement isatechniquewhichisused
to reduce the background noise present in the speech signal.
The noises are additive noise, echo, reverberationandspeaker
interference. The aim of the proposed method is to reduce the
background noise present in the speech signal by using
compressive sensing. The goal of compressive sensing is to
compress the speech signal at transmitter and decompress it
at the receiver from far less samples than the nyquist rate. In
this work, a speech signal is taken and then it is compressively
sampled using a measurement matrix which in case is
composed of randomly generated numbers. The output of the
compressed sensing algorithm is the observationvector which
is transmitted to the receiver. At the receiver section, signal is
reconstructed from a significant small numbers of samples by
using l1- minimization. MATLAB simulationsareperformed to
compress the speech signal below the nyquist rate and to
reconstruct it without losing any important information.
Key Words: Speech enhancement, Compressive sensing,
DCT, l1 –minimization, Measurement matrix.
1. INTRODUCTION
In recent years, various signal sampling schemes have been
developed. However, such sampling methods are difficult to
implement. So before sampling the signal it should have
sufficient information about the reconstruction kernel. The
emerging compressive sensing theory shows that an
unevenly sampled discrete signal can be perfectly
reconstructed by high probability of success by using
different optimization techniques and by considering fewer
random projections or measurements compared to the
Nyquist standard. Amart Sulong et al proposed the
compressive sensing method by combining randomized
measurement matrix with the wiener filter to reduce the
noisy speech signal and thereby producing high signal to
noise ratio [1]. Joel A. Tropp et al demonstrated the
theoretical and empirical work of Orthogonal Matching
Pursuit (OMP) which is effective alternative to (BP) for
signal recovery from random measurements [2]. Phu Ngoc
Le et al proposed an improved soft – thresholding method
for DCT speech enhancement [3]. Vahid Abolghasemi
focused on proper estimation of measurement matrix for
compressive sampling of the signal [4].
2. Compressive sensing
Compressive sensing involves recovering the speech signal
from far less samples than the nyquist rate [8]. Fig.1 shows
the basic block diagram of compressive sensing. Initially,the
signal is sampled using nyquist rate, whereas with the help
of compressive sensing the signal is sampled below the
nyquist rate [5]. The signal is transformed into a domain in
which it shows sparse representation. Then the signal is
transmitted and stored in the channel by the receiver side
[13].
Fig.1 Basic block diagram of compressive sensing
Finally the signal is reconstructed from thesamplesbyusing
one of the different optimization techniques available.
3. Noizeus Corpus
Thirty sentences from the IEEE sentence database (IEEE
Subcommittee 1969) were recorded in a sound-proof booth
using Tucker Davis Technologies (TDT) recording
equipment [12]. The sentenceswereproduced bythreemale
and three female speakers. The sentences were originally
sampled at 25 kHz and down sampled to 8 kHz and eight
basic noise signals under different environmental conditions
are taken from the AURORA database [9]. It has the
recordings from different places like Babble, Car, Exhibition
hall, Restaurant, Street, Airport, Train station and Train.](https://image.slidesharecdn.com/irjet-v4i3272-171222104226/85/Speech-Enhancement-Using-Compressive-Sensing-1-320.jpg)
![International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1126
4. Proposed Method for Speech
Enhancement Using Compressive Sensing
algorithm
The proposed speech enhancement algorithm using
compressive sensing is illustrated in Fig.2
Analysis filter bank uses gammatone filter due to its
resemblance to the shape of human auditory filters. Then
discrete cosine transform is chosen due to its simplicity.
Subband modification is applied to produce subband
coefficients for analysing the speech signal. On synthesis
side, for solving convexoptimizationofcompressivesensing,
the gradient projection of sparse reconstructionalgorithmis
used [1]. Higher the processing power, higher is the quality
of the signal synthesized.
Fig.2 Flowchart for Proposed Speech Enhancement
Algorithm
5. Measurement Matrix
A random matrix is a matrix with random entries. A random
matrix (sometimes stochastic matrix) is a matrix-valued
random variable, in which some matrix or all of whose
elements are random variables.
y = Φx = ΦΨα (1)
Where, Φ is a M N measurement matrix with each row be
a measurement vector
α is the coefficientvector withKnonzeroeselement.
The measurement matrix plays a major roleintheprocess of
recovering the original signal. In compressive sensing there
are two types of measurement matrices namely, random
measurement matrix and the predefined measurement
matrix [14].
subject to Φx= y (2)
which is also known as basis pursuit (P1).
= (3)
It is otherwise known as Taxicab norm Manhattan norm [2].
The distance obtained from this norm is called the
Manhattan distance or l1 distance.
6. Optimization Techniques
Signal reconstruction plays an major role in compressive
sensing theory where the signal is reconstructed or
recovered from a less number ofmeasurements[4].Byusing
optimization techniques it is possible to recover the signal
without losing the information at the receiver.
6.1. l1 Minimization
l1 minimization is used to solve the under determined
linear equations or sparsely corrupted solution to an over
determined equations [11].
7. Conventional Thresholding
In the proposed method soft thresholding is followed due to
its advantages [3].The soft thresholding is defined as
Ysoft =](https://image.slidesharecdn.com/irjet-v4i3272-171222104226/85/Speech-Enhancement-Using-Compressive-Sensing-2-320.jpg)
![International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1129
The speech signal was reconstructed without losing
important information that leads to increase in data rate.
Some of the future works are as follows. Different
transformations need to be tested in order to find the most
efficient one for this application. A measurementmatrixthat
will be optimum for speech signals is to be designed. The
proposed method has to be tested with other existing
methods to prove its efficiency.
10. References
[1] Amart Sulong, Teddy Surya Gunawan,OthmanO.Khalifa,
Mira Kartiwi,‘ Speech Enhancement based on Wiener
filter and Compressive Sensing’, Indonesian Journal of
Electrical Engineering and Computer Science, Vol. 2,
issue.2, pp. 367-379, 2016.
[2] Joel A. Tropp and Anna C. Gilbert, ‘Signal Recovery from
Random Measurements via Orthogonal Matching
Pursuit’, IEEE Transactions on Information Theory, pp.
4655- 4666, Dec 2007.
[3] Phu Ngoc Le, Eliathamby Ambikairajah and Eric Choi,
‘An Improved Soft Threshold Method for DCT Speech
Enhancement’, IEEE, pp. 268-271, July 2008.
[4] Vahid Abolghasemi, Saideh Ferdowsi, Bahador
Makkiabadi, and Saeid Saneis, ‘On Optimization of the
Measurement matrix for Compressive Sensing’, 18th
European Signal Processing Conference (EUSIPCO-
2010), semantic scholar, pp. 427-431, Aalborg,
Denmark ,Aug 2010.
[5] Amart Sulong, Teddy S.Gunawan, OthmanO.Khalifa,and
Jalel Chebil, ‘Speech Enhancement based on
Compressive Sensing’, 5th International Conference on
Mechatronics (ICOM’13), pp. 1-10. 2013.
[6] Anna maria jose and Mathurakani M, ‘Compressive
Sensing Based OFDM Channel Estimation’, International
Journal of Modern Sciences and Engineering
Technology, Vol. 3, issue. 2, pp.13-20, 2016.
[7] Donoho D.L, ‘Compressed Sensing’, IEEE Transactions
on Information Theory, vol. 52, pp.1289-1306, April
2006.
[8] Emmanuel J. Candes and Michael B. Wakin, ‘An
Introduction to Compressive Sampling’, IEEE Signal
Processing Magazine, Vol. 25, issue 2, pp. 21-30, March
2008.
[9] Hirsch H and Pearce D (2000),
‘The Aurora Experimental Framework for the
Performance Evaluation of Speech Recognition Systems
under Noisy Conditions’, ISCA ITRW ASR2000.
[10] Jagdeep Kaur, Kamaljeet Kaur, Monika Bharti, Pankaj
Sharma and Jatinder Kaur ‘Reconstruction Using
Compressive Sensing: A Review’, International Journal
of Advanced Research in Computer and
Communication Engineering, Vol.2, issue.9, pp.3648-
3650,2013.
[11] Massimo Fornasier and Holger Rauhut, ‘Compressive
Sensing’, Springer link handbook of mathematical
methods and imaging, pp. 187-228, 2010.
[12] IEEE Subcommittee 1969 IEEERecommendedPractice
for Speech Quality Measurements. IEEE Trans. Audio
and Electroacoustics, AU-17(3), 225-246.
[13] Pooja C. Nahar, Dr. Mahesh and Kolte.T, ‘An
Introduction to Compressive Sensing and its
Applications’, International Journal of Scientific and
Research Publications, Volume 4, Issue 6, pp . 1-5, June
2014.
[14] Richard G. Baraniuk,‘CompressiveSensing’,IEEESignal
Processing Magazine, lecture notes, pp.118-120, 124,
2007.
[15] Siddhi Desai and Prof. Naitik Nakrani ‘Compressive
Sensing in Speech Processing: A Survey Based on
Sparsity and Sensing Matrix’, International Journal of
Emerging Technology and Advanced Engineering,
Volume 3, Issue 12, pp . 18-23,2013.
[16] Sabir Ahmed, ‘Compressive sensing for speech signals
in mobile systems’, The University of Texas at Tyler,
pp.1-51, 2011.](https://image.slidesharecdn.com/irjet-v4i3272-171222104226/85/Speech-Enhancement-Using-Compressive-Sensing-5-320.jpg)
Speech Enhancement Using Compressive Sensing
- 1. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1125 Speech Enhancement using Compressive Sensing K.Kiruthiga1, J.Indra2 1PG Scholar,Dept. Of EIE, Kongu Engineering College, Tamilnadu,India 2Assistant Professor (SLG),Dept. Of EIE, Kongu Engineering College, Tamilnadu, India ---------------------------------------------------------------------***----------------------------------------------------------------- Abstract - Speech enhancement isatechniquewhichisused to reduce the background noise present in the speech signal. The noises are additive noise, echo, reverberationandspeaker interference. The aim of the proposed method is to reduce the background noise present in the speech signal by using compressive sensing. The goal of compressive sensing is to compress the speech signal at transmitter and decompress it at the receiver from far less samples than the nyquist rate. In this work, a speech signal is taken and then it is compressively sampled using a measurement matrix which in case is composed of randomly generated numbers. The output of the compressed sensing algorithm is the observationvector which is transmitted to the receiver. At the receiver section, signal is reconstructed from a significant small numbers of samples by using l1- minimization. MATLAB simulationsareperformed to compress the speech signal below the nyquist rate and to reconstruct it without losing any important information. Key Words: Speech enhancement, Compressive sensing, DCT, l1 –minimization, Measurement matrix. 1. INTRODUCTION In recent years, various signal sampling schemes have been developed. However, such sampling methods are difficult to implement. So before sampling the signal it should have sufficient information about the reconstruction kernel. The emerging compressive sensing theory shows that an unevenly sampled discrete signal can be perfectly reconstructed by high probability of success by using different optimization techniques and by considering fewer random projections or measurements compared to the Nyquist standard. Amart Sulong et al proposed the compressive sensing method by combining randomized measurement matrix with the wiener filter to reduce the noisy speech signal and thereby producing high signal to noise ratio [1]. Joel A. Tropp et al demonstrated the theoretical and empirical work of Orthogonal Matching Pursuit (OMP) which is effective alternative to (BP) for signal recovery from random measurements [2]. Phu Ngoc Le et al proposed an improved soft – thresholding method for DCT speech enhancement [3]. Vahid Abolghasemi focused on proper estimation of measurement matrix for compressive sampling of the signal [4]. 2. Compressive sensing Compressive sensing involves recovering the speech signal from far less samples than the nyquist rate [8]. Fig.1 shows the basic block diagram of compressive sensing. Initially,the signal is sampled using nyquist rate, whereas with the help of compressive sensing the signal is sampled below the nyquist rate [5]. The signal is transformed into a domain in which it shows sparse representation. Then the signal is transmitted and stored in the channel by the receiver side [13]. Fig.1 Basic block diagram of compressive sensing Finally the signal is reconstructed from thesamplesbyusing one of the different optimization techniques available. 3. Noizeus Corpus Thirty sentences from the IEEE sentence database (IEEE Subcommittee 1969) were recorded in a sound-proof booth using Tucker Davis Technologies (TDT) recording equipment [12]. The sentenceswereproduced bythreemale and three female speakers. The sentences were originally sampled at 25 kHz and down sampled to 8 kHz and eight basic noise signals under different environmental conditions are taken from the AURORA database [9]. It has the recordings from different places like Babble, Car, Exhibition hall, Restaurant, Street, Airport, Train station and Train.
- 2. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1126 4. Proposed Method for Speech Enhancement Using Compressive Sensing algorithm The proposed speech enhancement algorithm using compressive sensing is illustrated in Fig.2 Analysis filter bank uses gammatone filter due to its resemblance to the shape of human auditory filters. Then discrete cosine transform is chosen due to its simplicity. Subband modification is applied to produce subband coefficients for analysing the speech signal. On synthesis side, for solving convexoptimizationofcompressivesensing, the gradient projection of sparse reconstructionalgorithmis used [1]. Higher the processing power, higher is the quality of the signal synthesized. Fig.2 Flowchart for Proposed Speech Enhancement Algorithm 5. Measurement Matrix A random matrix is a matrix with random entries. A random matrix (sometimes stochastic matrix) is a matrix-valued random variable, in which some matrix or all of whose elements are random variables. y = Φx = ΦΨα (1) Where, Φ is a M N measurement matrix with each row be a measurement vector α is the coefficientvector withKnonzeroeselement. The measurement matrix plays a major roleintheprocess of recovering the original signal. In compressive sensing there are two types of measurement matrices namely, random measurement matrix and the predefined measurement matrix [14]. subject to Φx= y (2) which is also known as basis pursuit (P1). = (3) It is otherwise known as Taxicab norm Manhattan norm [2]. The distance obtained from this norm is called the Manhattan distance or l1 distance. 6. Optimization Techniques Signal reconstruction plays an major role in compressive sensing theory where the signal is reconstructed or recovered from a less number ofmeasurements[4].Byusing optimization techniques it is possible to recover the signal without losing the information at the receiver. 6.1. l1 Minimization l1 minimization is used to solve the under determined linear equations or sparsely corrupted solution to an over determined equations [11]. 7. Conventional Thresholding In the proposed method soft thresholding is followed due to its advantages [3].The soft thresholding is defined as Ysoft =
- 3. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1127 8. Experimental Results and Discussions 8.1. Input Speech and Noise Representation in Time Domain The sample sentence is “Clams are small, round, soft and tasty” (i). Enhanced Output from Babble Noise (0db) The enhanced output from babble noiseisshownintheFig.4 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 input clean signal Length of the input speech signal Amplitudeoftheinputspeechsignal (a) 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 babble noise at 0db signal Length of the noisy signal Amplitudeofthenoisysignal (b) 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Discrete cosine transform of 0db signal Length of the DCT spectrum AmplitudeoftheDCTspectrum (c) 0 200 400 600 800 1000 1200 1400 1600 1800 2000 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 The Threshold spectrum The length of the threshold spectrum Amplitudeofthethresholdspectrum (d) Random Measurement matrix 500 1000 1500 2000 100 200 300 400 500 600 700 800 -0.1 -0.05 0 0.05 0.1 (e) 0 100 200 300 400 500 600 700 800 -0.1 -0.05 0 0.05 0.1 0.15 Observation Vector (f) Fig.4 Enhanced Output From Babble Noise at(0db)(a)Clean Speech (b) Noisy Speech (c) Applying DCT (d) Thresholding (e) Random MeasurementMatrix(f)OutputforCompressive Sensing Figure 4, shows input clean speech signal in (a) and then adding clean speech and babble noise at 0db which is composed of 2000 samples in (b), The recorded speech signal goes through DCT which transforms the sequence of
- 4. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1128 real data points into real spectrum and is shown in (c). The threshold window is then applied to eliminate the small coefficients as shown in (d). Threshold spectrum is multiplied by measurement matrix which is composed of randomly generated numbers as shown in (e), and then compressive sensing algorithm is used in (f). Table 1: Amount of signals compressed by using signal parameters NOISE SIGNAL AT DIFFERENT (DB) LENGTH OF THE SIGNAL (L) THRESHOLD WINDOW UL LL COMP ESSED SAMP LE(K) ERRO R(%) COMPRES SION(%) (K/L) Babble 0db 2000 0.04 -0.06 800 0.1089 40%5db 2000 0.04 0.04 -0.06 -0.06 0.1361 10db 2000 0.04 -0.06 0.1931 15db 2000 0.04 -0.06 0.1821 Airport 0db 2000 0.04 -0.06 800 0.1037 40% 5db 2000 0.04 -0.06 0.1900 10db 2000 0.04 -0.06 0.1777 15db 2000 0.04 -0.06 0.1975 Car 0db 2000 0.04 -0.06 800 0.0795 40% 5db 2000 0.04 -0.06 0.1738 10db 2000 0.04 -0.06 0.2193 15db 2000 0.04 -0.06 0.1963 Table 2: Amount of signals compressed by using signal parameters NOISE SIGNAL AT DIFFERENT (DB) LENGTH OF THE SIGNAL (L) THRESHOLD WINDOW UL LL COMP RESSE D SAMPL E(K) ERRO R (%) COMPR ESSION( %) (K/L) Babble 0db 2000 0.04 -0.06 800 0.1047 40% 5db 2000 0.04 -0.06 0.0802 10db 2000 0.04 -0.06 0.0810 15db 2000 0.04 -0.06 0.1179 Airport 0db 2000 0.04 -0.06 800 0.0835 40% 5db 2000 0.04 -0.06 0.0708 10db 2000 0.04 -0.06 0.0608 15db 2000 0.04 -0.06 0.0693 Car 0db 2000 0.04 -0.06 800 0.1273 40% 5db 2000 0.04 -0.06 0.0717 10db 2000 0.04 -0.06 0.0568 15db 2000 0.04 -0.06 0.0746 From Table 1, it is observed that for babble noise with noise level as 5db, length of the signal as 2000, threshold window from 0.04 to -0.06 and compressed samplesas800,the error is 13.61% and compression is upto 40%. From Table 2, it is observed that for babble noise with noiselevel as5db,length of the signal as 2000, threshold window from 0.04 to -0.06, and compressed samples as 800, the error is 8.02% and compression is upto 40%. Table 3: Amount of Signals Compressed by using Signal Parameters NOISE SIGNAL AT DIFFERENT (DB) LENGTH OF THE SIGNAL (L) THRESHOLD WINDOW UL LL COMP RESSE D SAMPL E(K) ERROR (%) COMP RESSIO N(%) (K/L) Babble 0db 2000 0.04 -0.06 800 0.0866 40% 5db 2000 0.04 -0.06 0.0863 10db 2000 0.04 -0.06 0.1009 15db 2000 0.04 -0.06 0.0887 Airport 0db 2000 0.04 -0.06 800 0.0894 40% 5db 2000 0.04 -0.06 0.0767 10db 2000 0.04 -0.06 0.0939 15db 2000 0.04 -0.06 0.0834 Car 0db 2000 0.04 -0.06 800 0.1410 40% 5db 2000 0.04 -0.06 0.0995 10db 2000 0.04 -0.06 0.0879 15db 2000 0.04 -0.06 0.0967 From Table 3, it is observed that for babble noise with noise level as 5db, length of the signal as 2000, threshold window from 0.04 to -0.06, and compressed samples as 800, the error is 8.63% and compression is upto 40%. 9. Conclusion and Future Scope During the design process, this module went through different tests and analysis in order to find the most adequate optimization technique to reconstruct the speech signal with few random measurements without losing the information. For simulation purposes, code was created in order to compress and transmit the speech signal below the Nyquist rate by taking only a few measurements of the signal. As a result, it shows that by keeping the length of the signal (L) and threshold window (Th) constant we can achieve the desired compression of the signal by making the signal sparse (K) to a certain amount whichinturnincreases the data rates. After multiple simulations, it was found that the system worked as expected and the speech signal was reconstructed efficiently with a minimum error.
- 5. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 03 | Mar -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1129 The speech signal was reconstructed without losing important information that leads to increase in data rate. Some of the future works are as follows. Different transformations need to be tested in order to find the most efficient one for this application. A measurementmatrixthat will be optimum for speech signals is to be designed. The proposed method has to be tested with other existing methods to prove its efficiency. 10. References [1] Amart Sulong, Teddy Surya Gunawan,OthmanO.Khalifa, Mira Kartiwi,‘ Speech Enhancement based on Wiener filter and Compressive Sensing’, Indonesian Journal of Electrical Engineering and Computer Science, Vol. 2, issue.2, pp. 367-379, 2016. [2] Joel A. Tropp and Anna C. Gilbert, ‘Signal Recovery from Random Measurements via Orthogonal Matching Pursuit’, IEEE Transactions on Information Theory, pp. 4655- 4666, Dec 2007. [3] Phu Ngoc Le, Eliathamby Ambikairajah and Eric Choi, ‘An Improved Soft Threshold Method for DCT Speech Enhancement’, IEEE, pp. 268-271, July 2008. [4] Vahid Abolghasemi, Saideh Ferdowsi, Bahador Makkiabadi, and Saeid Saneis, ‘On Optimization of the Measurement matrix for Compressive Sensing’, 18th European Signal Processing Conference (EUSIPCO- 2010), semantic scholar, pp. 427-431, Aalborg, Denmark ,Aug 2010. [5] Amart Sulong, Teddy S.Gunawan, OthmanO.Khalifa,and Jalel Chebil, ‘Speech Enhancement based on Compressive Sensing’, 5th International Conference on Mechatronics (ICOM’13), pp. 1-10. 2013. [6] Anna maria jose and Mathurakani M, ‘Compressive Sensing Based OFDM Channel Estimation’, International Journal of Modern Sciences and Engineering Technology, Vol. 3, issue. 2, pp.13-20, 2016. [7] Donoho D.L, ‘Compressed Sensing’, IEEE Transactions on Information Theory, vol. 52, pp.1289-1306, April 2006. [8] Emmanuel J. Candes and Michael B. Wakin, ‘An Introduction to Compressive Sampling’, IEEE Signal Processing Magazine, Vol. 25, issue 2, pp. 21-30, March 2008. [9] Hirsch H and Pearce D (2000), ‘The Aurora Experimental Framework for the Performance Evaluation of Speech Recognition Systems under Noisy Conditions’, ISCA ITRW ASR2000. [10] Jagdeep Kaur, Kamaljeet Kaur, Monika Bharti, Pankaj Sharma and Jatinder Kaur ‘Reconstruction Using Compressive Sensing: A Review’, International Journal of Advanced Research in Computer and Communication Engineering, Vol.2, issue.9, pp.3648- 3650,2013. [11] Massimo Fornasier and Holger Rauhut, ‘Compressive Sensing’, Springer link handbook of mathematical methods and imaging, pp. 187-228, 2010. [12] IEEE Subcommittee 1969 IEEERecommendedPractice for Speech Quality Measurements. IEEE Trans. Audio and Electroacoustics, AU-17(3), 225-246. [13] Pooja C. Nahar, Dr. Mahesh and Kolte.T, ‘An Introduction to Compressive Sensing and its Applications’, International Journal of Scientific and Research Publications, Volume 4, Issue 6, pp . 1-5, June 2014. [14] Richard G. Baraniuk,‘CompressiveSensing’,IEEESignal Processing Magazine, lecture notes, pp.118-120, 124, 2007. [15] Siddhi Desai and Prof. Naitik Nakrani ‘Compressive Sensing in Speech Processing: A Survey Based on Sparsity and Sensing Matrix’, International Journal of Emerging Technology and Advanced Engineering, Volume 3, Issue 12, pp . 18-23,2013. [16] Sabir Ahmed, ‘Compressive sensing for speech signals in mobile systems’, The University of Texas at Tyler, pp.1-51, 2011.