Chao Li,Ting Jiang,Sheng Wu

School of Information and Communication Engineering,Beijing University of Posts and Telecommunications,Beijing 100876,China

Abstract: Aiming at the problem of music noise introduced by classical spectral subtraction,a shorttime modulation domain (STM) spectral subtraction method has been successfully applied for singlechannel speech enhancement.However,due to the inaccurate voice activity detection (VAD),the residual music noise and enhanced performance still need to be further improved,especially in the low signal to noise ratio (SNR) scenarios.To address this issue,an improved frame iterative spectral subtraction in the STM domain(IMModSSub)is proposed.More specifically,with the inter-frame correlation,the noise subtraction is directly applied to handle the noisy signal for each frame in the STM domain.Then,the noisy signal is classified into speech or silence frames based on a predefined threshold of segmented SNR.With these classification results,a corresponding mask function is developed for noisy speech after noise subtraction.Finally,exploiting the increased sparsity of speech signal in the modulation domain,the orthogonal matching pursuit (OMP) technique is employed to the speech frames for improving the speech quality and intelligibility.The effectiveness of the proposed method is evaluated with three types of noise,including white noise,pink noise,and hfchannel noise.The obtained results show that the proposed method outperforms some established baselines at lower SNRs(-5 to+5 dB).

Keywords: short-time modulation domain; singlechannel speech enhancement; modulation improved frame iterative spectral subtraction;low SNRs

I.INTRODUCTION

Speech communication plays a vital role in human life[1],such as smartphone communications,speechoperated machines,hearing aids,military communications,and automatic speech recognition systems.However,in the process of speech information transmission,it is inevitably to be corrupted by ubiquitous background noise,which will severely degrades the communication quality and the speech naturalness of human listeners[2].Hence,the recover of the damaged speech signal is a non-trivial task.The speech enhancement technique focuses on removing or attenuating a significant amount of background noise from the corrupted speech while keeping the overall quality and intelligibility of speech and reducing the effect of noise as much as possible[3].With the development of the enhancement process,the numerous enhancement methods have been developed,which can be loosely divided into two categories,namely single-channel speech enhancement and multi-channel speech enhancement[4,5].Among others,singlechannel speech enhancement has attracted extensive attention of researchers due to its simplicity and effectiveness.

In fact,in the past few decades,a growing number of popular single-channel speech enhancement algorithms have been designed,such as spectral subtraction(SS)[6],filtering-based approaches[7],minimum mean-square error (MMSE)-based techniques[8,9],wavelet shrinkage[10]and the sought-after deep learning[11,12].Most of them exploit the analysis-modification-synthesis (AMS) framework to enhance the corrupted speech in the acoustic domain.The AMS framework,as the name implies,is comprised of three parts:(1)the short-time Fourier transform(STFT)is utilized to analyze the polluted speech signal in the analysis stage;(2)the enhancement algorithm only modifies the amplitude spectrum without changing the phase in the modification stage;(3)both the inverse STFT (ISTFT) and overlap-add (OLA)synthesis process are employed to achieved the enhanced speech in the synthesis stage[13].Even today,these enhancement techniques are still widely considered for speech enhancement due to their remarkable performance.

Recently,many speech processing techniques,such as speech coding[14],speaker recognition[15],speech recognition[16],and speech enhancement[17],have been widely used in the modulation domain.Owing to the psychological and physiological experimental evidence,the emergence of this phenomenon is supported.For example,the authors of[18],suggested that the faithful representation of the signal in the modulation domain was essential to our speech perception,because the perceptual filtering in the modulation domain was analogous to our perception of temporal dynamics.Physiological experiments indicated that all levels of the mammalian auditory system had a special sensitivity to the amplitude modulation of the narrow-band acoustic signal[19].The authors of[20],made use of the low-pass and high-pass filters to point out that the frequency range of the modulation domain lies within 4-16 Hz was important for the intelligibility of speech,especially the region around 4-5 Hz.Similarly,the authors of[21]have pointed out that the low modulation bands carried the most speech information.Furthermore,numerous related studies about speech perception and psychoacoustics showed the fact that the overall quality and intelligibility of speech signal mainly exist in the slowly changing modulation information[22].As a consequence,it would be intriguing to perform the enhancement technique in the modulation domain.

Spectral subtraction is one of the most widely used and the simplest enhancement methods in the acoustic domain[23].Hence,it was the first typical enhancement technique to be extended in the short-time modulation(STM)domain by the authors of[24].The modulation spectrum subtraction (ModSSub) technique achieved the desired enhanced speech by subtracting the modulation noise energy spectrum from the modulation noisy energy spectrum.It suppressed the annoying music noise of spectral subtraction by increasing the modulation frame duration.Due to the remarkable improvement achieved by ModSSub,the modulation domain enhancement approach has become one of the mainstream methods.In subsequent work,the authors of[25]suggested that the shorter modulation frame duration (MFD) was beneficial to improve the overall quality and intelligibility of speech signal.Motivated by this result,a shorter MFD is employed to the MMSE technique in the STM domain[26].As a consequence,it effectively improves the ModSSub process,which needs to select the appropriate smoothing parameters to reduce the music noise.The experimental results show that the performance of the MMSE technique in the STM domain is significantly better than that in the acoustic domain.However,the speech distortion will be introduced by replacing clean speech with the noisy phase in the signal to noise ratio(SNR)is less than 8 dB[27].To address this issue,the authors of[28],developed a novel modulation MMSE method,which utilized the real and imaginary parts of corrupted speech in the modulation AMS framework.A subspace-based speech enhancement method was applied in the STM domain[29],which did well work on the colored noise.The authors of[30]proposed a high-dimensional Wiener filter in the STM domain and utilized the non-iterative decision-directed technique to estimate the noise spectrum.This work achieved a good performance by enhancing the textures of the output signal.The authors of[31]performed the codebook-based noise and speech estimation in the STM domain,which improved the performance of enhancement in the non-stationary noise cases.What’s more,numerous other popular speech enhancement approaches in the acoustic domain,such as Bayesian noise estimation[32],Kalman filtering[33],wavelet denoising method[34]and compressive speech enhancement[35],have been also extended to the STM domain.However,the enhancement performances of these algorithms in poor SNR situations scenarios is far from being stratified and required to be further improved.This is the main motivation of this paper.

Inspired by the increased sparsity in the STM domain[35],we invoke the compressed sensing (CS)technique to improve the ModSSub method in low SNR conditions.More specifically,by exploiting the correlation between each frame[36],the improved frame-iterative spectral subtraction is implemented in the STM domain (i.e.,IModSSub).Note that the required noise estimation depends on the selected segment SNR (segSNR) threshold.The CS reconstruction is then employed to further attenuate the impact of residual noise by the noise subtraction in each modulation frame.Lastly,the two ISTFT and OLA synthesis are carried out to construct the enhanced speech signal.However,a noticeable problem has arisen that it may fail to improve the quality of the re-synthesized speech signal and the resulting denoising effect is less than outstanding.To cope with this issue,a mask function based on the segSNR threshold is performed to the frame noisy signal in the modulation domain.Moreover,the orthogonal matching pursuit (OMP) technique is employed to the speech frames for improving the speech quality and intelligibility.

The contributions of our work can be summarized from four aspects:(1) To the best of the authors’ knowledge,the mask-based IModSSub (IMModSSub) approach is the first time developed for the single-channel speech enhancement.(2) Our improved method mainly exploits the increased sparsity of the speech signal in the STM domain for improving the performance of ModSSub approach.(3)A corresponding mask function based on the predefined threshold value of segSNR is developed for the noisy signal,which dramatically reduces the number of frames to be reconstructed and significantly improves the ability of speech denoising.(4) Experimental results reveal that the IMModSSub approach can perform considerably better than several standard baselines for different types of noise(Gaussian noisewhite noise,colored noise-pink noise,and real world noise-hfchannel noise) in the healthy noise levels (-5 dB to+5 dB).

The rest of this paper is organized as follows.In Section II,the AMS framework for speech enhancement in the frequency domain is briefly recapitulated.After that,the speech enhancement approach based on IMModSSub is described in Section III.In Section IV,an experimental study comparing our improved approach with other approaches is provided.Finally,Section V concludes the paper.

II.THE AMS FRAMEWORK FOR SPEECH ENHANCEMENT IN THE FREQUENCY DOMAIN

In this section,we will introduce the AMS framework for speech enhancement in the frequency domain,which provides the basic structure employment in the modulation domain.Here,we consider that a clean speech is additively distorted by an uncorrelated noise signal,which results in an additive noise model,i.e.,

wherey(t),x(t),andv(t) denote the noisy speech,the clean speech,and the noise signal in the time domain,respectively.Due to the short-term stability of the speech signal,the noisy speech needs to be processed by STFT and we arrive at

wheref{·}is the STFT function,andY(l,k) represents the short-time frequency representation ofy(t).Here,landkdenote the time frame index and frequency bin index,respectively.Trefers to the length of each frame,which is equal to the fast Fourier transform(FFT)size.Prefers to the time frame advance,andw(t)denotes the acoustic analysis window.In the enhancement approach,the range of short-time frame length generally lasts around 10-40 ms.The Hamming or Hanning window is typically employed as the acoustic analysis window.Then,the STFT representation of(1)is

whereX(l,k) andV(l,k) are served as the STFT representation of the clean speech and the noise signal,respectively.The STFT representations of them have two parts:the magnitude spectrum and the phase spectrum.For example,the polar form ofy(t)in the time-frequency(T-F)domain is given by

where|Y(l,k)|and ∠Y(l,k)are served as the magnitude spectrum and phase spectrum ofY(l,k),respectively.

In the AMS framework,the magnitude spectrum of enhanced speech signal can be obtained from the magnitude spectrum of noisy speech by the speech enhancement technique,while the phase spectrum of the enhanced speech signal is replaced by that of the noisy signal.Hence,the polar form of the enhanced speechS(l,k)in the modification stage can be written as

where|Z(l,k)|and ∠Y(l,k)are the magnitude spectrum and phase spectrum of enhanced speechS(l,k),respectively.Furthermore,S(l,k) can also be obtained by the spectral gain function,which is given by

III.SPEECH ENHANCEMENT BASED ON IMMODSSUB

This section will describe the IMModSSub-based single-channel speech enhancement,which can significantly improve the visible residual noise and the speech quality suffering from the IModSSub and ModSSub approach.More specifically,the formulation of this problem is presented before describing the optimized IMModSSub algorithm.

3.1 Problem Formulatio n

The speech enhancement task will be described in this subsection.More specifically,the intention to achieve the enhanced speech signal from the noisy speech is developed in the STM domain,which can take advantage of the increased sparsity to improve the performance of the ModSSub approach.First,the spectrum of the STM,is computed by carrying out STFT analysis on each frequency component of the STFT form of the(2).Hence,the noisy speech spectrumY(c,k,m)in the STM domain is calculated as

wherec,k,andmare served as the STM frame index,the acoustic frequency index,and the STM frequency index,respectively,and mod{·}refers to the STM function.Moreover,the symbolLrefers to MFD,and the symbolP1represents the modulation frame overlap,theu(l) denotes the STM analysis window function (Hamming or Hanning window).Similarly,following the same form with (4),the polar form ofY(c,k,m)can be written as

where|Y(c,k,m)|and ∠Y(c,k,m)denotes the STM magnitude spectrum and the STM phase spectrum of noisy speech,respectively.Similarly,the STM magnitude spectrum of the estimated clean speech (i.e.,can be achieved by the IMModSSub method.The noisy STM phase spectrum is used as the estimated clean speech STM phase spectrum.As a consequence,the modified STM spectrum of the estimated enhanced speechcan be given as

To clearly describe the enhancement process,we let the STM spectrum of the enhanced speech be obtained by the modulation spectral gain function,we have

Figure 1. The IMModSSub-based speech enhancement framework.

3.2 Optimized Algorithm for IMModSSub

The core idea of the IMModSSub approach is inspired by the fact that the increased sparsity in the STM domain[35],and the success of the CS-based spectral subtraction[37]approach for single-channel speech enhancement in the acoustic domain.However,owing to the inaccuracy of noise estimation and the need of reconstructing a great quantity of speech frames,the denoising performance is far from being outstanding.Thus,we will describe the segSNR-based mask function to overcome this limitation.

3.2.1 IModSSub approach

The ModSSub[24]approach has been successfully applied to single-channel speech enhancement.However,its denoising performance needs to be further improved,especially under strong noise conditions.Here,we adopt the IModSSub approach,which exploits the inter-frame correlation and the increased sparsity in the STM domain to cope with the issue of ModSSub.In the following discussions,the IModSSub approach will be introduced in detail in the remainder of this section.

The classical spectral subtraction[6]in the acoustic frequency domain has been extended to the STM domain in[24],i.e.,ModSSub.The enhanced modulation magnitude spectrum can be given as

Note that the application ofρandcan greatly improve the flexibility of spectral subtraction.The authors of[6]suggest that the value of over subtraction factorρ,i.e.,

whereρ0=4,andλ=6.67.Note that segSNR(c,k)is the SNR value of a frame in the STM domain.Giving as

In (12) and (15),when segSNR(c,k)＜ μ,is achieved by applying the averaging rule and inter frame correlation,such that

whereαis a smoothing factor used for improving the accuracy of the noise estimation,the symbolμis an empirically determined threshold value of segSNR.Besides,the initial noise estimation is given by

wherecini= 1,...,cn,andcnare the initial noise frames which do not contain speech.However,owing to the inaccurate noise estimation and the increased sparsity of speech signal in the STM domain,the CS-based enhancement technique[37]is employed to further improve the denoising performance of the ModSSub technique.The CS-based speech enhancement will be described as follows

where the number of elements 1 in each row is determined by the reciprocal of the compression ratioFor the speech enhancement,(19) can be also written as the additive noise model,i.e.,

whereS1(c,k,m)is the modulation enhanced speech by CS technique,andV1(c,k,m)is the residual noise from the ModSSub method.According to the different sparsity of speech signal and the noise signal in the STM domain[35],we adopt the simple and faster orthogonal matching pursuit (OMP) technique to achieve our desired sparse speech signal,which can achieve the purpose of further enhancement.The problem of OMP optimization can be expressed as

Algorithm 1.The IModSSub approach for speech enhancement.Input: y(t),ϖ,cn,μ,B,N;Output: S1(t);1: Y(l,k)=f{y(t)};2:for k =1,...,K do 3: Y(c,k,m)=f{Y(l,k)};4: |ˆV(cint,k,m)|= 1 images/BZ_114_723_725_771_771.pngcnc=1|ˆV(c,k,m)|;5:for c=1,...,C do 6:Perform(12)and(13);7:if segSNR(c,k)＜μ then 8:Perform(16);9:end if 10:Zy(c,k,m)=Φ(c,k)|ˆZ1(c,k,m)|;11:Zy(c,k,m)=Zs1(c,k,m)+Zv(c,k,m);12:Get |S1(c,k,m)| by OMP with corrmaxand ε;13:end for 14: S1(c,k,m)=|S1(c,k,m)|ej∠Y(c,k,m);15: |S1(c,k)|is obtained by ISTFT and OLA synthesis;16:end for 17: S1(c,k)=|S1(c,k)|ej∠Y(c,k);18: S1(t)is obtained by ISTFT and OLA synthesis.cn

where‖·‖1and‖·‖2arel1-norm andl2-norm[39],respectively.|S1(c,k,m)|is the magnitude spectrum ofS1(c,k,m).Note thatεis an error threshold,which is as close as possible to the residual noise level of the modulated frame.However,since the estimated noise of each modulation frame is different,resulting the residual noise is different as well.When the reconstruction errorεis fixed,the enhancement performance is not attractive.To cope with this issue,we develop a correlation threshold method,which has been proved to achieve an excellent fitting correlation effect.Specifically,the OMP algorithm carries out the threshold processing on the maximum correlation thresholdcorrmaxin the process of reconstructing and screening related atoms.Here,we refer to the exponential fitting used in[37]to obtain the correlation threshold,it can be expressed as

3.2.2 the segSNR-based mask function

Due to the inaccuracy of the noise estimation and the maximum correlation coefficient thresholdcorrmaxin the Algorithm 1,the improvement of denoising performance by IModSSub is not pronounced.Therefore,we introduce a segSNR-based mask function tofor further reducing the impact of music noise.The segSNR-based mask function M(c,k,m)is given by

whereμ1is an empirical constant which depends on the noise type andpriorisegSNR.Although a largerμ1reduces more residual noise,it causes more speech distortion.Therefore,the value of the thresholdμ1has to be set for striking a balance between them.Then,the mask function M(c,k,m)is performed forto obtain

where the multiplication of M(c,k,m) andis preformed in an element-wise manner.Then,the CS approach is performed to the active-speech frame (i.e.,M(c,k,m) = 1).The process is expressed as

where|S(c,k,m)|represents the STM magnitude spectrum of further the enhanced speech in each active-speech frame.Note that|S(c,k,m)|is likewise obtained by OMP withcorrmaxandεin(22)and(23).However,the active-noise frames(i.e.,M(c,k,m) =0)do not require the employment of the CS approach.It can be given that

Algorithm 2.The segSNR-based mask function for speech enhancement.Input: |ˆZ1(c,k,m)|,μ1;Output: S(c,k,m);1:for c=1,...,C do 2:if segSNR(c,k)＞μ1 then 3:M(c,k,m)=1;4:|ˆZ2(c,k,m)|=M(c,k,m)|ˆZ1(c,k,m)|;5:Zy2(c,k,m)=Φ(c,k)|ˆZ2(c,k,m)|;6:S(c,k,m) is obtained by OMP with corrmaxand ε;7:else 8:M(c,k,m)=0;9:|ˆZ2(c,k,m)|=M(c,k,m)|ˆZ1(c,k,m)|;10:|S(c,k,m)|=|ˆZ2(c,k,m)|;11:end if 12:end for 13: S(c,k,m)=|S(c,k,m)|ej∠Y(c,k,m).

Then,the twice ISTFT and OLA synthesis with unchanged noisy phase is carried out to achieve the final enhanced speechS(t).This approach of segSNRbased mask function for further speech enhancement,i.e.,IMModSSub,is summarized in Algorithm 2.

IV.EXPERIMENTS AND DISCUSSION

In this section,our purpose is to examine the effectiveness of our improved approach (i.e.,IMModSSub) in low SNR scenarios and compare the performances against fvie commonly used and established baseline methods:a non-causalprioriSNRbased MMSE method (MMSE_NPS)[8],aprioriSNR-based Wiener fliter (Wiener_TPS)[40],Spectral subtraction (SSBerouti)[6],ModSSub[24],and IModSSub.All the methods are compared in Gaussian white noise,color noise (pink noise),and real world noise(hfchannel noise)conditions.

4.1 Experimental Settings

In the following experiments,a total of 30 clean speech signals (sp01-sp30) are obtained from the NOIZEUS database[41],which are applied as the test clean speech.More specifically,this test database including 30 different sentences with a sampling frequency at 8 kHz,which are obtained from six people (i.e.,three females and three males).Moreover,the Gaussian white noise and the non-Gaussian noises(pink,hfchannel noise) are served as additive noises for testing.All the noises are obtained from the NOISEX-92 database[42].Additionally,the test clean speech signals are degraded by these different noises at poor noise levels(i.e.,-5,-2,0,2,and 5 dB).Note that the noise needs to be down-sampled to 8 kHz.Due to the short-term stability of the speech,the duration of the acoustic frame is 32 ms.The length of the frame overlap is 16 ms,which is taken to ensure the speech continuity.For the STM domain,the slurring effect will be from the longer MFD,while the music noise will be from the shorter MFD[24].Here,we set the MFD to 192 ms.Both the window function of the acoustic and STM domain are the Hamming window,which are applied to suppress the Gibbs phenomenon.The spectral floor level parameterϖis set to 0.002.The empirically determined threshold value of segSNR,i.e.,μ=2.2 dB,and the value ofμwill be changed with the types of noise.The smoothing factor isα= 0.9[6].In order to further reduce the number of samples while ensuring the quality of speech reconstruction,the compression ratio is set to 0.5.

If he favours you, he will take you to Waq of Qaf; if not, you will never get there, for seven seas are on the way, and they are such seas that if all the kings of the earth, and all their wazirs, and all their wise men considered for a thousand years, they would not be able to cross them

4.2 Performance Metrics

In this subsection,we will briefly introduce three widely used objective performance measures.All of them are utilized to describe and examine the performance of different enhancement approaches,namely,the segSNR[27],the perceptual evaluation of speech quality (PESQ)[41],and the short-time objective intelligibility measure (STOI)[27],respectively.The segSNR measure is utilized to examine the ability to suppress noise,and the calculation is described as

wheres(l) andx(l) are served as thel-th frame of the reconstructed speech and clean speech signal in the time-domain,respectively.The index setLmeans the speech signal frames.As a result,a higher value of segSNR indicates better noise suppression.

In contrast to the segSNR metric,both the PESQ objective metric and the STOI objective metric are significantly related to the human audition system.PESQ is widely adopted to predict the speech distortion by computing the disturbance betweenx(t) ands(t) with a variable value within[−0.5,4.5],and the higher value indicates the better quality ofs(t).STOI is widely utilized to predict the human speech intelligibility by calculating the correlation of short-time temporal envelopes betweenx(t)ands(t).The value range is[0,1].Similarly,the higher value indicates the better human speech intelligibility ofs(t).It is also worth noting that all these objective evaluation measures are calculated by the average of 30 test sentences.

4.3 Experimental Results and Discussions

4.3.1 The performance comparison between improved SSBerouti and IModSSub

This subsection will provide the performance comparisons between the improved SSBerouti (ISSBerouti) method and the IModSSub technique.The test clean speech signal (sp01) is degraded by the Gaussian white noise.The performance comparisons are given in Table 1.As shown in in Table 1,it can be concluded that the CS-based spectral subtraction technique in the STM domain,i.e.,IModSSub,significantly outperforms that of the acoustic domain approach(ISSBerouti)in terms of the segSNR improvements,especially at poor SNRs(-5,-2 and 0 dB).This is because,in this case,the magnitudes of the residual noise peaks become much smaller,and the sparsity of speech signals in the STM domain increases.Besides,the inter-frame correlation is also considered to improve the denoising performance.Additionally,the STM method achieves improvements than that achieved by the ISSBerouti technique at -2 and 0 dB noise levels.However,the PESQ scores of the IModSSub approach are very close to the ISSBerouti technique at -5,2,and 5 dB SNRs.Regarding the results of another objective measure STOI,the IModSSub approach also performs consistently better than that achieved by the SSBerouti technique.Nonetheless,it has a little loss compared to the original noisy speech at -5 dB noise level.It is due to the fact that the healthy noise level drowns out the clean speech,the speech sparseness negligible.

4.3.2 The performance in the Gaussian white noise situation

In this subsection,we will show and discuss the performance comparisons between the proposed IMModSSub algorithm and the baselines in the Gaussian white noise situation.The comparisons are presented in Table 2.

As the comparisons indicated in Table 2,it can be observed that these three objective measures (i.e.,segSNR,PESQ,and STOI),improve with the increased of the input SNR level.In terms of the average segSNR,shown in Table 2,the IMModSSub method outperforms other methods across the input SNR range from -5 dB to 5 dB.Moreover,the improvements achieved by the IMModSSub approach are more pronounced in lower input noise levels (-5 dB,-2 dB)than that in higher levels(2 dB,5 dB).It is interesting to observe that the result of the IModSSub approach is slightly improved compared with that of ModSSub.It is because that the setting of maximum correlation thresholdcorrmaxin the acoustic domain is developed in STM domain may not be accurate.In terms of the average PESQ scores,as presented in Table 2.The IMModSSub approach performs the remarkably best average PESQ scores than that of the other methods at low input noise levels(-5 dB-2 dB).However,it is comparable with the scores achieved by the IModSSub method.Additionally,the average PESQ scores of the Wiener_TPS method does not increase with the SNRs,which implies that the Wiener_TPS method will fail in adverse conditions.in Table 2 shows the average STOI scores of different methods.It is noted that significantly scores are obtained by the SSBerouti method.The second best performance is achieved by the IModSSub algorithm.This is because that we are mainly interested in the speech quality enhancement,while the enhanced speech intelligibility techniques is not applied.Generally speaking,the proposed IMModSSub approach has better objective evaluation scores than that of the baselines in the Gaussian noise scenario,especially at the lower SNR case.

Table 1. The performance comparison between ISSBerouti and IModSSub.

The reconstructed waveforms of the test clean speech (“sp01”) by the aforementioned enhancement techniques.The clean speech is corrupted by the additive Gaussian white noise at-5 dB SNR.The reconstructed waveforms as showing in Figure 2.

From Figure 2,we can observe that our approach yields a significantly better waveform than that of other approaches.This is duo to the fact that the segSNR-based mask function can suppress the residual noise as much as possible without reducing thespeech quality.However,there is a small distortion achieved by the hard mask (0 or 1).In contrast to our proposed approach,both the waveforms of the MMSE_NPS and the Wiener_TPS methods have a notable speech distortion.Moreover,the SSBerouti technique has an amount of residual noise.reasons are as follows:both MMSE-NPS and Wiener-TPS performances are sensitive to the accurate noise covariance estimation.As a consequence,the condition will be lost in the poor SNRs.In addition,the similar noise suppression is performed by ModSSub and IModSSub.Comparatively,the proposed approach has better performance than that of baselines in the adverse noise environment.

Figure 2. The reconstructed waveform comparisons of clean speech(“sp01”)achieved by different approaches in the case of white noise at-5 dB SNR.

Figure 3. The reconstructed waveform comparisons of clean speech(“sp01”)achieved by different approaches in the case of pink noise at-5 dB SNR.

4.3.3 The performances in some non-Gaussian noise situations

This subsection will compare the average segSNR,the average PESQ scores,and the average STOI scores of our proposed approach with the baselines(MMSE_NPS,Wiener_TPS,SSBerouti,ModSSub,and IModSSub approaches) in several non-Gaussian noise (i.e.,colored pink noise and hfchannel noise).First,to evaluate the suppression of colored noise and real-world noise.We show the average segSNR of theIMModSSub method and baselines in Table 3.

Table 2. The performance comparisons between the proposed IMModSub method and baselines in Gaussian white noise.

As the comparison in Table 3,the IMModSSub method has impressive results compared with other enhancement algorithms in terms of average segSNR improvements.However,the improved approach can achieve slightly better than that of the other approaches at a higher noise level(5 dB).we also can observe that both the IModSSub and ModSSub methods show a nearly the same noise suppression effect.Note that the SSBerouti technique is close to failing at -5 dB SNR.This is because the case that the voice activity detection(VAD)mistakenly classifies noise frames into speech frames.Nonetheless,this confusion will be improved with increased input SNR.From Table 3,we notice that the Wiener_TPS achieves the higher average segSNR than other baselines (MMSE_NPS,SSBerouti,ModSSub,and IModSSub methods)in the range of -5 dB to -2 dB.It is also observed that the average PESQ scores of the improved approach and baselines for monaural speech enhancement in the colored noise(pink noise)and real-world noise(hfchannel noise).In contrast to the segSNR improvements and the STOI scores,the PESQ scores are widely applied to evaluate the reconstructed speech signal’s overall quality.The average PESQ scores are shown in Table 4.

From the results in Table 4,one should note that the better improvements,in terms of average PESQ scores,are still obtained by our proposed methods in lower hfchannel noise conditions (-5 dB,-2 dB,and 0 dB),but not in the pink noise conditions.This table clearly displays that the ModSSub approach achieves the best average PESQ scores than the other approaches in the low input SNR range (i.e.,0 dB-5 dB).However,the IModSSub approach achieves the best performance at lower SNRs (-2 dB and -5 dB).Moreover,our approach achieves great improvement with the increase of input SNRs.This is because that the set of a threshold for the mask function is fixed and needs to be further improved.In Table 4,it should be noted that the proposed approach can achieve higher average PESQ scores than that achieved by the othermethods at various input noise levels (from -5 dB to 5 dB).We think this is because of the test hfchannel noise within the stationary noise.

Table 3. The average segSNR of IMModSSub and baselines in some non-Gaussian noises.

Table 4. The average PESQ scores of IMModSSub and baselines in some non-Gaussian noises.

Finally,the another objective measure (i.e.,the STOI metric) is taken to observe the speech intelligibility,which are achieved by the above mentioned approaches in some non-Gaussian noise scenes.The comparisons of average STOI scores are shown in Table 5.Observing the performance in Table 5,we can find that our improved approach is worse than the SSBerouti method.This is because of the importance of phase in poor SNRs[43].Although the operation of using noisy phase to replace the phase of enhanced speech signal is not ideal in terms of intelligibility at low SNR,the loss of intelligibility is within the acceptable range,which avoids complex phase calculation.From Table 5,the IMModSSub has almost the same average STOI scores as the ModSSub method at-2 dB and 5 dB.This reveals that the taken mask technology still has a specific role in the pink noise condition.Unfortunately,the performance of the IMModSSub method needs to be further improved in lower SNRs(-5 dB,-2 dB).As the average STOI scores shown in Table 5,our proposed approach is capable of working well in the real world noise at lower noise levels(-2 dB and 0 dB).Additionally,due to the poor VAD technique,the Wiener_TPS approach achieves the lowest average STOI scores.Nonetheless,it is noted that we are mainly interested in improving the speech perceived quality and the ability of boosting noise.In order to achieve better speech intelligibility,our future work will be the improvement of the poor performance which occurs sometimes in terms of the STOI measure.

Table 5. The average STOI scores of IMModSSub and baselines in some non-Gaussian noises.

Figure 3 shows the comparisons of reconstructed waveforms of the clean speech (“sp01”),which are achieved by different single-channel speech enhancement methods.The test speech is degraded by the pink noise at-5 dB noise level.

As the comparisons in Figure 3,the MMSE-NPS and Wiener_TPS approaches have a disappointing loss of the information of clean speech (“sp01”).This is because the preconditions of these methods,such as the additive noise needs to obey Gaussian distribution and should be stationary noise,which are broken in strong pink noise level(-5 dB).The SSBerouti approach seems to have a lot of residual noise.Unfortunately,the reconstructed waveforms are achieved by the modulation methods(IMModSSub,IModSSub,and ModSSub) have some speech information lost in 1.5s.However,our proposed approach has a better denoising ability at -5 dB SNR.Comparatively,our proposed approach can obtain a better-reconstructed waveform than the established baselines at-5 dB SNR.Nevertheless,our future work will also focus on improving the distortion of the clean speech information.

V.CONCLUSION

In this work,we proposed an improved modulation enhancement approach,namely,IMModSSub,which can achieve a good performance for suppressing noise in the modulation domain.More specifically,exploiting the increased sparsity in the STM domain,we employed the OMP optimization algorithm to further improve the performance of the ModSSub approach.Moreover,a segSMR-based mask function was developed for the noisy speech after noise subtraction for each frame,which enhanced the ability to suppress noise and improved the overall quality of the recovered speech signal.The experimental results demonstrated that the improved approach performed significantly better than the five baseline approaches in terms of the segSNR and PESQ measure at strong noise levels.Significantly,in the case of white noise,the segSNR score of our presented approach could improve about 1.08 dB than ModSSub at-5 dB SNR.The PESQ score was improved about 0.16 than the SSBerouti technique at 0 dB SNR.The STOI score was improved around 0.08 than MMSE_NPS at 2 dB SNR.Similarly,as for the colored noise and real-world noise conditions,our proposed approach could also yield a higher PESQ and segSNR score than those achieved by the baselines.It is worth pointing out that our proposed approach has a low complexity without a loss of the significant speech perceived quality and intelligibility.Even more impressively,our proposed approach does not require the accurate VAD technique and a prior knowledge of the additive noise.

ACKNOWLEDGEMENT

This work was supported by National Natural Science Foundation of China(NSFC)(No.61671075)and Major Program of National Natural Science Foundation of China(No.61631003).