speech processing research paper 15

IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICPART B: CYBERNETICS, VOL. 37, NO. 4, AUGUST 2007 877

A Generalized TimeFrequency Subtraction Methodfor Robust Speech Enhancement Based on WaveletFilter Banks Modeling of Human Auditory System

Yu Shao and Chip-Hong Chang, Senior Member, IEEE

AbstractWe present a new speech enhancement scheme for asingle-microphone system to meet the demand for quality noisereduction algorithms capable of operating at a very low signal-to-noise ratio. A psychoacoustic model is incorporated into thegeneralized perceptual wavelet denoising method to reduce theresidual noise and improve the intelligibility of speech. The pro-posed method is a generalized timefrequency subtraction al-gorithm, which advantageously exploits the wavelet multiratesignal representation to preserve the critical transient informa-tion. Simultaneous masking and temporal masking of the humanauditory system are modeled by the perceptual wavelet packettransform via the frequency and temporal localization of speechcomponents. The wavelet coefficients are used to calculate theBark spreading energy and temporal spreading energy, fromwhich a timefrequency masking threshold is deduced to adap-tively adjust the subtraction parameters of the proposed method.An unvoiced speech enhancement algorithm is also integratedinto the system to improve the intelligibility of speech. Throughrigorous objective and subjective evaluations, it is shown thatthe proposed speech enhancement system is capable of reducingnoise with little speech degradation in adverse noise environmentsand the overall performance is superior to several competitivemethods.

Index TermsAuditory masking, noise reduction, speech en-hancement, wavelet.

I. INTRODUCTION

AUTOMATIC speech processing systems are increasinglyemployed in real-world applications, such as hands-freecar kits, communicators in noisy cockpits, and voice-activateddialers for cellular phones [1], [18], [23], [24], [33], [35], butthe performance of these devices in many practical situationsdegrades drastically when confronted with a great diversity ofadverse noise conditions such as background noise and micro-phone distortions. Thus, there is a strong demand for qualitynoise reduction algorithms capable of operating at very lowsignal-to-noise ratio (SNR) in order to combat various formsof noise distortion. Many solutions have been developed to dealwith the noise reduction problem. Generally, these solutions canbe classified into two main areas: nonparametric and statistical-model-based speech enhancements. Methods from the first

Manuscript received May 3, 2006; revised October 17, 2006. This paper wasrecommended by Associate Editor C.-T. Lin.

The authors are with the Centre for High Performance Embedded Systems,Nanyang Technological University, Singapore 63755 (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TSMCB.2007.895365

category usually remove an estimate of the distortion from thenoisy features, such as subtractive-type algorithms [34], andwavelet denoising [8]. The second category, statistical-model-based speech enhancement [10], utilizes a parametric model ofthe signal generation process. The parametric model normallydescribes the predictable structures and the expected patterns inthe signal process [6].

In this paper, the proposed speech enhancement system isbased on subtractive-type algorithms. It estimates the short-time spectral magnitude of speech by subtracting the noiseestimation from the noisy speech. The main attractions ofspectral subtraction are: 1) its relative simplicity, in that it onlyrequires an estimate of the noise power spectrum, and 2) itshigh flexibility against subtraction parameters variation. Fromthe basic approach of spectral magnitude subtraction introducedby Boll [4], many derivatives have been developed, such aspower spectral subtraction [3], nonlinear spectral subtraction[34], generalized spectral subtraction [26], multiband spectralsubtraction [13], spectral subtraction based on priori SNR[11], spectral subtraction based on the masking properties ofthe human auditory system [33], and single-channel speechenhancement based on a recurrent neural network [15]. How-ever, the main problem in spectral subtraction is the presenceof processing distortions caused by the random variations ofnoise. Musical residual noise is introduced in subtractive-typedenoising methods, which will degrade the perceptibility ofthe processed speech. To reduce the effect of residual noise, anumber of methods were considered: Boll [4] proposed magni-tude averaging; Berouti et al. [3] proposed the oversubtractionof noise and defined a spectral floor to make residual noiseinaudible; McAulay and Malpass [21] proposed soft-decisionnoise suppression filtering; Ephraim and Malah [9] proposed aminimum mean-square-error short-time spectral amplitude es-timator; Vaseghi [34] introduced nonlinear spectral subtraction;Virag [33] made use of masking properties of the human audi-tory system to reduce the effect of residual noise; and Hu andLoizou [12] proposed a speech enhancement method by incor-porating the psychoacoustical model in the frequency domain.However, the performances of the above methods are not satis-fying in adverse environments, particularly when the SNR isvery low. The reason is that in very low SNR conditions, itis difficult to suppress noise without degrading intelligibility,and without introducing residual noise and speech distortion.Therefore, processed speech can be even less perceptible thanthe original noisy speech. The methods that adopt the maskingproperty of the human auditory system can reduce the effectof residual noise, but the drawback is the large computational

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878 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICPART B: CYBERNETICS, VOL. 37, NO. 4, AUGUST 2007

effort associated with the subband decomposition and theadditional FFT analyzer required for psychoacoustic modeling.Furthermore, they do not make use of the temporal maskingmodels.

In order to simplify the mapping of audio signals into a scalethat could well preserve the timefrequency related informa-tion, the wavelet packet transform (WPT) has been incorporatedrecently in some proposed speech and audio coding systems[20]. Sinha and Tewfik [25] first introduced adapted wavelets totransparent audio compression; Srinivasan and Jamieson [29]proposed a high-quality audio compression using the adaptivewavelet packet decomposition and psychoacoustic modeling;Bahoura and Rouat [5] proposed modified wavelet speech en-hancement based on the teager energy operator. This techniquedoes not require an explicit estimation of the noise level ora priori knowledge of the SNR, which is usually needed inmany popular speech enhancement methods. Li et al. [14]proposed the perceptual timefrequency subtraction algorithmfor noise reduction in hearing aids. Veselinovic and Graupe [32]introduced a wavelet transform approach to the blind adaptivefiltering of speech from unknown noises. It can reduce thenoise effect well, but the complexity is high. Lu and Wang [16]applied the critical band WPT to speech enhancement.Ayat et al. [2] proposed a wavelet-based speech enhancementusing the step-garrote thresholding algorithm. However, thequalities of the processed speech of the above methods degradeas the distortion is introduced and the high-frequency speechsignals are grievously reduced by wavelet transform.

The objective of this paper is to introduce a versatile speechenhancement method based on the human auditory model. Theemphases are on the reduction of the effect of residual noiseand speech distortion in the denoising process and the enhance-ment of the denoised speech in high frequency to improveits intelligibility. The proposed speech enhancement systemconsists of two main functions. One is a generalized percep-tual timefrequency subtraction (GPTFS) method based on themasking properties of the human auditory system. The GPTFSworks in conjunction with a perceptual WPT (PWPT) to reducethe effect of noise contamination. The other is an unvoicedspeech enhancement (USE), which tunes a set of weights inhigh-frequency subbands to improve the intelligibility of theprocessed speech. The following contributions have been made.

The first contribution is the use of PWPT to approximate24 critical bands of the human auditory system up to 16 kHz.It enables the components of a complex sound to be appro-priately segregated in frequency and time in order to mimicthe frequency selectivity and temporal masking of the humanauditory system. Previous method used WPT to approximatecritical bands only up to the range of 8 kHz for telephonequality speech [25]. Critical high-frequency components innoisy speech have been analyzed by our proposed PWPT to im-prove the perceptual quality of the final processed speech. Thesecond contribution is a parametric formulation of subtractivenoise reduction based on the generalized perceptual wavelettransform. We refers to the Fourier transform-based gain func-tion of the generalized spectral subtraction method [33] andderive the close form expressions for the subtraction factorand noise flooring factor, respectively, to optimize the tradeoffin the simultaneous reduction of background noise, residualnoise and speech distortion. These parameters of GPTFS can

then be adaptively tuned according to the noise level and themasking thresholds derived from the human auditory modelin wavelet domain. Finally, a new system structure for speechenhancement is developed to integrate GPTFS and USE inwavelet domain. The ability to process signal in both time andfrequency domains of the USE in the wavelet domain makes thediscrimination of the original speech in high-frequency bandsfrom noise possible, hence further improve the intelligibility ofspeech.

The rest of this paper is structured as follows. In Section II,a perceptual wavelet filter bank architecture is proposed toapproximate the critical band division of the human auditorysystem. In Section III, simultaneous and temporal maskings areunified and mapped onto the wavelet domain. These maskingproperties are then encapsulated in a parametric formulation ofGPTFS algorithm derived in Section IV. An adaptive speechenhancement system incorporating both GPTFS algorithm andUSE is presented. Rigorous evaluations and comparisons ofthe proposed method against other speech enhancement tech-niques under a wide variety of adverse conditions have beenperformed, using both objective and subjective measures. Theresults are presented and discussed in Section V. Section VIconcludes this paper.

II. PROPOSED ARCHITECTURE FOR PERCEPTUALWAVELET FILTER BANK

To design effective algorithm for enhancing speech, it needsa well build psychoacoustic model of the ear, which has anunsurpassed capability to adapt to noise. In this section, wepropose a new human auditory model that adopts the basestructure of traditional auditory model but replace the time-invariant bandpass filters with WPT in order to mimic thetimefrequency analysis of the critical bands according to thehearing characteristics of human cochlea.

A PWPT is used to decompose the speech signal from20 Hz to 16 kHz into 24 frequency subbands that approximatethe critical bands. The decomposition is implemented with anefficient seven-level tree structure. The analysis filter bank isdepicted in Fig. 1. In the proposed wavelet packet decompo-sition, the two-channel wavelet filter banks are used to splitboth the low-pass and high-pass bands [28] as opposed to onlythe decomposition of low-frequency bands in the usual waveletdecomposition. This binary tree decomposition is attractive dueto the following reasons [30]. First, the smoothness property ofwavelet is determined by the number of vanishing moments.If a wavelet with a large number of vanishing moments isused, the stringent bandwidth and stopband attenuation ofeach subband, as specified by the human auditory model, canbe more closely approximated by the wavelet decomposition.Second, the psychoacoustic study of human ears suggests thata frequency to bark transformation needs to be performed toaccurately model the frequency dependent sensitivity of humanears. Such a transformation is accomplished in audio processingsystems by dividing the frequency range into critical bands.

The 24 critical bands are derived from the perfect recon-struction filter bank with finite-length filters [28] using differentwavelets for the analysis and synthesis scaling functions. LetH(z) and G(z) be the lowpass (LP) and highpass (HP) transferfunctions, respectively, before the decimation-by-two operation

SHAO AND CHANG: GENERALIZED TIMEFREQUENCY SUBTRACTION METHOD 879

Fig. 1. Perceptual wavelet packet decomposition tree.

in each stage of the analysis filter bank. Further, let F (z) andJ(z) be the LP and HP transfer functions, respectively, afterthe upsampling-by-two operation in each stage of the synthesisfilter bank. The analysis and synthesis filter banks are relatedby [28]

g(n) = (1)nf(n) G(z) = F (z)j(n) = (1)nh(n) J(z) = H(z). (1)

The relationship between the LP and HP filters reducesthe number of filters to be implemented for each stage of thetwo-channel filter bank by half. Once the LP filters, H(z)and F (z) are designed, the HP filters, G(z) and J(z) can bederived from (1).

There are 24 critical bands in the hearing range of 016 kHz.Owing to the property of frequency selectivity related to criticalband, temporal resolution of the human ear, and regularityproperty of wavelets [25], Daubechies wavelet basis is chosenas prototype filter and a seven-stage WPT (the number of stagesjmax = 7, the frame length, Fjmax = 128, the frame length atstage j is given by Fj = 2j) is adopted to build perceptualwavelet filterbank. Wjk, represents WPT coefficient, where kis the coefficient number; j is the transform stage from whichWjk is chosen; l is the number of temporal coefficients inthe critical band. Table I shows the mapping of the PWPTcoefficients in each stage.

Table II shows the comparison of lower (fL) and upper(fu) frequencies, center frequency (fc) and bandwidth (f) inhertz between the critical band rate and the proposed perceptualwavelet packet tree scale.

TABLE IPERCEPTUAL WAVELET FILTER-BANKS COEFFICIENTS

TABLE IICRITICAL BAND RATE Z AND PERCEPTUAL WAVELET FILTER-BANKS W

Fig. 2 depicts the difference in the critical band rate betweenthe critical bands and the proposed perceptual wavelet packettree structural bands. The referenced critical band rate ZB inBark is approximated by [36]

ZB= 13 tan1(7.6 104f)+ 3.5 tan1(1.33 104f)2 (2)

where the frequency, f , is measured in hertz.


Fig. 2. Center frequencies of critical bands and perceptual wavelet packetdecomposition tree.

Fig. 3. Bandwidths of critical bands and perceptual wavelet packet decompo-sition tree.

The bandwidths of the critical bands and the perceptualwavelet packet tree are plotted in Fig. 3. From Fig. 3, itis evident that the critical bands have constant width atapproximately 100 Hz for center frequencies up to 500 Hz,and the bandwidths increase as the center frequency increasesfurther. The referenced critical bandwidth (CBW) in hertz iscalculated by [36]

CBW(f) = 25 + 75(1 + 1.4 106f2)0.69. (3)Fig. 4 compares the absolute threshold of hearing (ATH) in

hertz, critical band scale, and perceptual wavelet packet scale.The ATH characterizes the amount of energy needed in a puretone such that it can be detected by a listener in a noiselessenvironment. The referenced absolute threshold is expressed interms of sound pressure level (SPL) in decibels, and it is plottedin Fig. 4 with the following equation [36]:

ATHSPL(f) = 3.64f0.8 6.5e0.6(f3.3)2 + 0.001f4. (4)

From the results tabulated in Table II and plotted in Figs. 24,it is evident that the proposed perceptual wavelet packet tree canclosely mimic the experiential critical bands. The parameters ofthe discrete WPT filter used to derive the plots of Figs. 24 aredetermined based on the auditory masking properties, and theywill be discussed in the next section.

Fig. 4. ATH in (a) frequency, (b) bark, and (c) perceptual wavelet packet treescales.

III. UNIFICATION OF SIMULTANEOUS AND TEMPORALMASKINGS IN WAVELET PACKET DOMAIN

The notion of a critical band is related to the phenomenonof auditory masking, whereby the perception of one sound isobscured by the presence of another in frequency or in time.There are two dominant types of masking. The simultaneousmasking is the masking between two concurrent sounds, and itis best modeled in the frequency domain. The temporal mask-ing is the masking of other sounds immediately preceding orfollowing a sudden stimulus sound, and it is usually modeled inthe time domain. After studying the limitations of a traditionalauditory model using a Fourier transform, we establish a uni-fication of the simultaneous and temporal maskings by meansof PWPT.

In subtractive-type of speech enhancement, the maskee isthe residual noise. To make it inaudible, it should lie belowthe masking threshold or threshold of just noticeable distortion[17]. Clean speech is ideal for the estimation of maskingthresholds. When clean speech is not accessible, the enhancedspeech processed by the spectral subtraction gives reasonablygood estimate of the clean signal. Since masking is mani-fested by a shift of auditory threshold in signal detectability,and loudness is an important attribute of auditory percep-tion, the noise masking threshold can be determined by thecharacteristics of the masker and maskee, the SPL and thefrequency of the masker. The noise masking threshold for aresidual noise maskee in each critical band can be calculated asfollows.

A. Time and Frequency Analysis Along the CriticalBand Scale

Our goals are to approximate the critical band analysisand estimate the auditory masking threshold using the PWPT.The resulting 24-band wavelet packet approximation of thecritical band rate and the bandwidth approximation have beenshown in Figs. 2 and 3. The input signal is decomposed intocritical bands scale for timefrequency analysis. The outputsof the perceptual wavelet filterbank are squared to obtain theBark spectrum energy and temporal energy, respectively. The


Bark energy spectrum EBark(ZW ) with 1 ZW 24 is com-puted as

EBark(ZW ) =kb

k=ka

W 2j,k(ZW ) (5)

where ka and kb are the coefficient indexes of the first and lasttransform coefficients referring to Table I. The temporal energyEtemp(n) with n = 0, 1, . . . , l(ZW ) 1 in each critical bandZW can be derived as

Etemp(n) = W 2j,(ka+n)(ZW ). (6)

B. Convolution With Spreading Function

In this step, the Bark spectrum energy and temporal energyare convoluted with the spreading function, respectively. Thespreading of Bark energy EBark(ZW ) is calculated by the con-volution of EBark(ZW ) with the linear version of SF(ZW ) [36]

EBark(ZW ) =1

l(ZW )

24m=1

EBark(m)SF(ZW m) (7)

where the spreading function SF(ZW ) in decibels models theinteraction of the masking signals between different criticalbands and can be deduced as follows [27]:

SF(ZW ) = a+ + u2

(ZW ZW (k) + c)

u2

d+ (ZW ZW (k) + c)2 (8)

where u and are, respectively, the upper and lower slopes indecibels per Bark; d is the peak flatness; a and c are the com-pensation factors needed to satisfy SF(0) = 1. k [1, 24] is aninteger critical band identifier. The critical band rate distanceZW ZW (k) varies from 24 to 24 Bark. The parametersof the spreading function, SF(ZW ), which are empiricallydetermined by the listening test, were set to = 30 dB/Bark,u = 25 dB/Bark, d = 0.3, c = 0.05, and a = 27.4.

The temporal masking can be modeled in terms of temporalenergy spreading across time. The temporal spreading energyEtemp(n) with n = 0, 1, . . . , l(ZW ) 1 can be obtained by theconvolution of the linear temporal spreading function SF(n)with the temporal energy, whose calculation is similar to (7)

Etemp(n) =l(ZW )1m=0

Etemp(m)SF(n N

l(ZW )m

)(9)

where SF(n) is a parameterized spreading function similar to(8) and can be deduced as follows:

SF(n) = a+ + u2

(n n(k) + c)

u2

d+ (n n(k) + c)2. (10)

Corresponding to the minimum frame duration Fmin, the pa-rameters of the spreading function SF(n) in decibels em-ployed were set to = 20 dB/Fmin(dB/ms), u = 10 dB/

Fmin(dB/ms), d = 0.3, c = 0.2, and a = 7.9 after several lis-tening tests.

C. Calculating the Relative Threshold OffsetNext, a relative threshold offset O(Zw) is subtracted from

each critical band. It is required to distinguish betweentonelike and noiselike components in speech to calculate therelative threshold offset. There are two types of noise maskingthreshold: the threshold of tone masking noise Ttmn, whereTtmn(ZW ) = E Bark 14.5 ZW dB, and the thresholdof noise masking tone Tnmt, where Tnmt(ZW ) = E Bark 5.5 dB. To determine whether the signal is tonelike or noiselike,the spectral flatness measure (SFM) is used. From this value, atonality coefficient [17] is generated

= min(SFMdB/SFMdBmin, 1) (11)

where is a ratio of the SFMdB, which is computed at thelast stage of the decomposition to the SFMdBmin, which is anentirely tonelike reference over a frame. Using , the relativethreshold offset O(Zw) in decibels [17] for each critical bandis calculated as

O(ZW ) = (14.5 + ZW ) + (1 ) 5.5. (12)

D. Renormalization and Comparison With the ATH

To unify the temporal and simultaneous maskings into oneformulation, a temporal masking factor j,k(ZW ) is introducedas follows:

jk(ZW ) = E temp(k ka)/W 2j,k(ZW ) (13)

where j,k(ZW ) 1 indicates the extent of temporal masking.If j,k(ZW ) = 1, no temporal masking is induced, otherwise,if j,k(ZW ) > 1, the temporal masking has occurred. By com-bining the simultaneous masking threshold EBark(ZW ) andthe temporal masking factor j,k(ZW ), the timefrequencymasking threshold in the critical band ZW can be determinedas follows:

Mj,k(ZW ) = 10log[EBarkjk(ZW )][O(ZW )/10]. (14)

Finally, Mj,k(ZW ) is compared to the ATH in each criticalband, and the maximum of each value is retained as Tj,k(ZW )

Tj,k(ZW ) = max (Mj,k(ZW ),ATH(ZW )) . (15)

The unification of the simultaneous and temporal maskingproperties of the human auditory system forms the basis ofour GPTFS technique. It works in conjunction with the PWPTprocessor and an USE unit toward a speech enhancementsystem.

IV. PROPOSED ADAPTIVE SPEECHENHANCEMENT SYSTEM

Variants of spectral subtraction method with varying sub-traction rules have been derived from different criteria [34].


Fig. 5. Architecture of the proposed speech enhancement system.

Most of these algorithms possess parametric forms to improvethe agility of their estimators. The focus is mainly on theerror function used to reduce the musical residual noise inspectral domain. These methods suffer from inevitable loss ofsome vital information that degrades the auditory perceptionof enhanced speech. In this section, we develop a new GPTFSmethod based on the PWPT and the human auditory perception.Its parametric formulation is derived from the basis of thegeneralized Fourier spectral subtraction algorithm of [34]. TheGPTFS algorithm incorporates most of the basic subtractionrules and realizes the subtraction in a broader timefrequencydomain. More crucial information has been preserved than inFourier transform domain, leading to better perceptual outputsthan existing subtraction algorithms.

The block diagram of the proposed speech enhancementsystem is shown in Fig. 5. After the noisy signal x[n] isdecomposed by PWPT, the transform sequence is enhanced bya subtractive-type algorithm to produce the rough speech esti-mate. This estimate is used to calculate a timefrequency mask-ing threshold. Using this masking threshold, a new subtractionrule, which is masking dependent, is designed to compute anestimation of the original speech. This approach assumes thatthe high-energy frames of speech will partially mask the inputnoise (high masking threshold), hence reducing the need fora strong enhancement mechanism. On the other hand, framescontaining less speech (low masking threshold) will undergo anoverestimated subtraction. To further improve the intelligibilityof processed speech, an USE is applied. Finally, the processedspeech is reconstructed by the inverse PWPT. The noise estima-tion is assumed to be available and is performed during speechpauses. The speech pause detection algorithm from Marzinzikand Kollmeier [20] is adopted for the noise spectrum estimationby tracking the power envelope dynamics. The speech pausedetection algorithm has been extended for subband processingon our proposed system.

A. Generalized Perceptual TimeFrequency Subtraction

Consider a noisy speech signal which consists of the cleanspeech additively degraded by noise

x[n] = s[n] + [n] (16)

where x[n] and s[n] are the noisy and original speech, respec-tively. [n] is the additive noise, which can be white or colored.Original speech and noise are assumed to be uncorrelated.

To capture the localized information of transient signal, thePWPT is applied to the noisy input speech, i.e., {wj,k(x)} =PWPT(x[n])

wj,k(x) = wj,k(s) + wj,k(), j=0, 1, . . . , jmax 1k=0, 1, . . . , 2j 1 (17)

where wj,k(x), wj,k(s), and wj,k() are the wavelet transformcoefficients of a noisy signal, clean signal, and noise, respec-tively. (j, k) in the subscript of w corresponds to its scale andtranslation indexes. jmax is the maximum number of levels ofwavelet decomposition.

By applying the power spectral subtraction method [34]in the wavelet domain, the estimated power of the enhancedspeech is given by

|wj,k(s)|2={|wj,k(x)|2|wj,k()|2 , if |wj,k(x)|2> |wj,k()|20, otherwise

(18)where |wj,k(s)|2, |wj,k(x)|2, and |wj,k()|2 are the estimates ofthe power wavelet coefficients of the noise-suppressed speechsignal, the noisy speech and the estimated noise, respectively,in the wavelet domain.

Since there is no prior knowledge of the parameters of s[n]and [n], and only x[n] is accessible, the noise power spectrumin (18) is to be estimated from the time-average noise mag-nitude during the period in which the speech signal is absent.The time-average noise spectrum can be obtained by [34]

|wi,j,k()|2= 0.9|wi1,j,k()|2+ 0.1|wi1,j,k(x)|2 (19)where the subscript i is the frame index.

The design takes into account that human speech is based onmixing voiced and unvoiced phonemes over time. The voicedphonemes last for 40150 ms and their power concentrates atbelow 1.5 kHz, whereas the unvoiced phonemes last for 1050 ms and their power concentrates at around 28 kHz. Hence,s[n] is nonstationary over time interval of above 250 ms, andthe noise [n] is assumed to be piecewise-stationary or morestationary than s[n], which is valid for most environmentalnoise encountered. With the above assumption, the input signalx[n] is divided into 128 samples.

Substituting (17) into (18), we have|wj,k(s)|2 = |wj,k(s) + wj,k()|2 |wj,k()|2

= |wj,k(s)|2 +(|wj,k()|2 |wj,k()|2

)

Noise Variations

+ wj,k(s)wj,k() + wj,k(s)wj,k()

Cross Products

. (20)

The wavelet power spectrum of the estimated speech signalincludes error terms due to the nonlinear mapping of spectralestimates, the variations of the instantaneous noise power aboutthe estimated mean noise power, and the cross products of theoriginal speech and noise. Since signal and noise are assumed to


be uncorrelated, and the noise wavelet coefficients are assumedto have zero mean, the expected value of the power spectrum ofthe estimated speech signal in the wavelet domain is given by

E[|wj,k(s)|2

]=E

|wj,k(s)|2 + (|wj,k()|2 |wj,k()|2)

Noise Variations

+ wj,k(s)wj,k() + wj,k(s)wj,k()

Cross Products

=E[|wj,k(s)|2

]. (21)

Equation (21) shows that the expected value of the instan-taneous power spectrum of estimated speech signal convergesto that of the noise-free signal. However, it is noted that fornonstationary signals, such as speech, the objective is to recoverthe instantaneous or short-time signal, and only a relativelysmall amount of averaging can be applied. Too much averagingwill obscure the temporal evaluation of the signal. The spectralsubtraction in (18) can be deemed as an adaptive attenuationof noisy speech according to the posteriori SNR of the noisyspeech signal to the estimated noise. A gain function, Gain(j, k)for the zero-phase wavelet spectral subtraction filter can bedefined such that its magnitude response is in the range between0 and 1, i.e.,

wj,k(s)=Gain(j, k) wj,k(x), 0Gain(j, k)1. (22)

Comparing (18) and (22), we have

Gain(j, k)=

1 |wj,k()|

2

|wj,k(x)|2=

1 1SNRpost(j, k) (23)

where SNRpost(j, k) = |wj,k(x)|2/|wj,k()|2 is the posterioriSNR, which is defined as the ratio of the wavelet powerspectrum of the noisy speech signal to that of the estimatednoise. In the low SNR case, the gain is set to zero when thewavelet power spectrum of the noisy speech is less than that ofthe estimated noise.

The gain function in (23) acts as a posteriori SNR-dependentattenuator in the timefrequency domain. The input noisyspeech is attenuated more heavily with decreasing posterioriSNR and vice versa with increasing posteriori SNR. This fil-tering function can be readily implemented since the posterioriSNR can be easily measured on the noisy speech. Although itcan effectively filter out the background noise from the noisyspeech, the processing itself introduces musical residual noise.This processing distortion is due to the random variation ofnoise spectrum and the nonlinear mapping of the negative orsmall-valued spectral estimate. To make this residual noiseperceptually white, Virag [33] introduced several flexiblesubtraction parameters. These subtraction parameters are cho-sen to adapt to a criterion associated with the human audi-tory perception. The generalized spectral subtraction methodin [33] is based on Fourier transform. It considers only thesimultaneous masking property of human auditory system, and

the adaptation parameters are empirically determined. In whatfollows, we will state the generalized timefrequency subtrac-tion method in the PWPT domain and derive the close formexpressions for its optimal adaptation parameters.

From (23), the gain function of Virags generalized spectralsubtraction algorithm [33] can be reexpressed in terms ofperceptual wavelet spectral coefficients as follows:

Gain(j, k)=

(1

[wj,k()wj,k(x)

]1)2, if

[wj,k()wj,k(x)

]1< 1+(

[wj,k()wj,k(x)

]1)2, otherwise.

(24)The PWPT-based gain function of (24) possesses the same

set of free parameters as that of [33], and their effects aresummarized as follows. 1) The subtraction factor ( 1)controls the amount of noise subtracted from the noisy signal.For full noise reduction, = 1 whereas for oversubtraction > 1. Oversubtraction allows the timefrequency spectrum tobe attenuated more than necessary. This factor should be appro-priately selected to provide the best tradeoff between residualnoise peaks and audible distortion. 2) The noise flooring factor(0 < 1) makes use of the addition of background noiseto mask the residual noise. It determines the minimum valueof the gain function. If this factor is increased, parts of theresidual noise can be masked, but the level of background noiseretained in the enhanced speech increases. 3) The exponent = 1 = 1/2 determines the abruptness of the transition frompure clean speech to pure noise in noisy speech. For magnitudesubtraction, 1 = 2 = 1 whereas for power subtraction, 1 =2, 2 = 0.5.

To formally select these adaptation parameters, we will opti-mize the fixed gain function of (23) by minimizing the speechdistortion and residue noise based on the masking thresholddetermined in Section III. To segregate the residual noise fromthe speech distortion, we define a differential wavelet coeffi-cient as the difference between the wavelet coefficients of theclean speech and the enhanced speech. The differential waveletcoefficients can be expressed as follows:

wj,k = wj,k(s) wj,k(s)=Gain(j, k) wj,k(x) wj,k(s)=wj,k(s)(Gain(j, k) 1)+Gain(j, k) wj,k(). (25)

The optimal gain function will be derived by following thesame approach as in [16]. The difference is that our gainfunction will be optimized based on the thresholding criterionthat correlate with both temporal and simultaneous maskings.The auditory perception is better approximated by using morecomplex wavelet basis and efficient filter bank structure. Thedifferential wavelet coefficients can be viewed as a linear super-position of speech distortion, j,k(s) and residual noise, j,k()in the wavelet domain, where the speech distortion, j,k(s) andresidual noise, j,k() are defined as

j,k(s) =wj,k(s) (Gain(j, k) 1) (26)j,k() =wj,k()Gain(j, k). (27)


The energies of the speech distortion and residual noise are,respectively, given by

Ej,k(s) =2j1k=0

|wj,k(s)|2 |(Gain(j, k) 1)|2 (28)

Ej,k() =2j1k=0

|wj,k()|2 |(Gain(j, k))|2 . (29)

Since the residual noise is not audible when its energy issmaller than the masking threshold, we will suppress only thewavelet coefficients of noisy speech when the noise level isgreater than the masking threshold as in [16]. To optimize thegain function, we minimize the energy of speech distortionin wavelet domain subjected to the constraint that the energyof residual noise is kept below the masking threshold. A costfunction J(j, k) can be formulated according to the energies ofthe speech distortion and residual noise expressed in terms ofwavelet coefficients.

J(j, k) = Ej,k(s) + j,k(ZW ) {Ej,k(s) Tj,k(ZW )

} (30)where the Largrangian multiplier of each subband, j,k(ZW )serves as a weighting factor to the residue noise.

Substituting (28) and (29) into (30), we have

J(j, k) =2j1k=0

|wj,k(s)|2 |(Gain(j, k) 1)|2 + j,k(ZW )

2j1k=0

|wj,k()|2 |(Gain(j, k))|2 Tj,k(ZW ) . (31)

The optimal gain function is obtained by minimizing thecost function J(j, k). Taking the derivative of the cost functionJ(j, k) with respect the Largrangian multiplier, j,k(ZW ) andset the result to zero, the optimal gain function is determined

dJ(j, k)dj,k(ZW )

=2j1k=0

|wj,k()|2 |(Gain(j, k))|2Tj,k(ZW )=0

Gainopt(j, k)= Tj,k(ZW )2j1

k=0

|wj,k()|2, 0 Gain(j, k) 1.

(32)

By equating the adaptive gain function of (24) to the optimalgain function of (32), and considering the power subtraction,i.e., 1 = 2 and 2 = 0.5, the closed-form expressions for thesubtraction parameters, and can be derived as follows:

1 1SNR(j, k) =Tj,k(ZW )

2j1k=0

|wj,k()|2

= SNR(j, k)

1 Tj,k(ZW )2j1

k=0

|wj,k()|2

(33)

1SNR(j, k) =Tj,k(ZW )

2j1k=0

|wj,k()|2

= SNR(j, k) Tj,k(ZW )2j1k=0

|wj,k()|2. (34)

Equations (33) and (34) ensure that the subtraction parame-ters and are adapted to the masking threshold of humanauditory system to achieve a good tradeoff between the residualnoise, speech distortion, and background noise. In high SNRcondition, the parameter is increased to reduce the residualnoise at the expense of introducing more speech distortion.On the contrary, in low SNR condition, the parameter isincreased to trade the residual noise reduction for an increasedbackground noise in the enhanced speech. To make the resid-ual noise inaudible, the subtraction parameters are set suchthat the residual noise stays just below the masking thresholdTj,k(ZW ). If the masking threshold is low, the subtractionparameters will be increased to reduce the effect of residualnoise. If the masking threshold is high, the residual noisewill naturally be masked and become inaudible. Therefore, thesubtraction parameters can be kept at their minimal values tominimize the speech distortion.

B. Unvoiced Speech Enhancement

The intelligibility of the processed speech is further im-proved by an USE (see Fig. 5). Although the GPTFS subsystemis useful for enhancing the portion of speech signal that containsmost of the signal energy, they sometimes degrade the high-frequency bands of low energy. To alleviate this problem, weapply a soft thresholding method to enhance the portion ofspeech signal that lies in the high-frequency bands [31].

Despite most energy of the speech signal is concentratedaround the lower frequency bands, the speech energy in thehigh-frequency range may possess considerably high peak andcarry crucial perception information. To enhance the portionof speech signal that lies in the high-frequency range withoutdegrading the performance of the overall system, the USEunequally weights the frequency bands to amplify only thosecomponents with detectable peaks in the high-frequency range.The timefrequency energy (TFE), which is estimated using thewavelet coefficients, is applied in this subsystem. The TFE iscomputed as

j,k =Fj

(wj,k(x))2

/ Fj maxn=1

x[n]2 (35)

where . is the norm operator. Fjmax is the total frame length.Fj is the frame length of each subband. The TFE mapping, is a normalized energy function of wavelet coefficients at eachposition of the binary tree. To estimate the enhanced originalspeech, we assume that the TFE of noise does not changemuch over time. Since only noisy observation is accessible, wecan only estimate the noise TFE by the minimum TFE of theobservation. The high-frequency TFE peak can be deduced as

j,k(s)=j,k(x)j,k()=j,k(x) min1mM

mj,k(x) (36)


where j,k(x) denote the TFE of the noisy speech which iscomposed of the TFEs of noise j,k() and the original speechj,k(s). The superscript m denotes the frame index. UnlikeGPTFS, which operates on each time frame, the USE spansover several frames, where M indicates the number of framescovered in this duration.

To amplify those high-frequency bands containing compo-nents of unvoiced speech without affecting all other high-frequency bands, we define a threshold j,k. Different waveletcoefficients of the processed speech are then emphasized viatheir weights, uj,k. The weight, uj,k is obtained by

uj,k=

1, j,k(s)j,k

(37)where the threshold j,k is determined empirically throughexperimentation, below which the subband is noise-free anduj,k is set to 1. Therefore, when the noise estimate approacheszero and the speech is strong enough, uj,k = 1. The weightedwavelet coefficients are given by

wj,k(s) = uj,k wj,k(s). (38)

GPTFS either amplifies or attenuates a particular frequencyband based on the estimated signal energy content in lowfrequency. When the SNR is high, the USE is effective. In thecase of low SNR, GPTFS have suppressed most energy of noisewhile significantly reduced the unvoiced speech at the sametime. Nevertheless, the succeeding USE can still coarsely es-timate the noise and tune a set of weights to somewhat enhancethe unvoiced speech. Finally, an inverse wavelet transform isapplied to resynthesize the enhanced speech

s[n] = IPWPT (wj,k(x)) (39)where IPWPT means inverse PWPT.

V. EXPERIMENTAL RESULTS

In this section, the proposed system is evaluated withspeeches produced in various adverse conditions and comparedagainst the following competitive methods: 1) speech enhance-ment method using perceptually constrained gain factors incritical-band-WPT (Lu04) [16]; 2) speech enhancement methodincorporating a psychoacoustical model in frequency domain(Hu04) [12]; 3) wavelet speech enhancement method basedon the teager energy operator (B&R01) [5]; 4) perceptualtimefrequency subtraction algorithm (Li01) [14]; 5) singlechannel speech enhancement based on masking properties ofhuman auditory system (Vir99) [33]; and 6) parametric spectralsubtraction (Sim98) [26]. The original speeches used for thetests were taken from the DARPA TIMIT Acoustic-PhoneticSpeech Database. Different background noises with differenttimefrequency distributions were taken from the Noisex-92database [37]. The tested noisy environments include whiteGaussian noise, pink noise, Volvo engine noise, F16 cockpitnoise, factory noise, high-frequency channel noise, and speech-like noise. Noise has been added to the clean speech signal with

Fig. 6. Comparison of different speech enhancement methods in whiteGaussian noise by (a) SNR improvement and (b) IS distortion.

different SNRs. The same speech pause detection algorithmfrom Marzinzik and Kollmeier [20] is used for all algorithmsbeing compared that require noise estimation. This speechpause detection algorithm has a low hit rate of 0.11 and 0.12,and a low false-alarm rate of 0.085 and 0.08 at SNR of 5 and10 dB, respectively, in the speechlike noise environment.

A. SNR Improvement and ItakuraSaito (IS) DistortionThe amount of noise reduction is generally measured in

terms of the SNR improvement, given by the difference be-tween the input and output segmental SNRs. The pre-SNR andpost-SNR are defined as

SNRpre=1K

K1m=0

20log10

1N

N1n=0

s(n+Nm)

1N

N1n=0

v(n+Nm)

(40)

SNRpost=1K

K1m=0

20log10

1N

N1n=0

s(n+Nm)

1N

N1n=0

(s(n+Nm)s(n+Nm))

(41)where K represents the number of frames in the signal and Nindicates the number of samples per frame.

The segment SNR improvement is defined as SNRpost SNRpre

SNRimp=1K

K1m=0

20log10

1N

N1n=0

(n+Nm)

1N

N1n=0

(s(n+Nm)s(n+Nm))

.

(42)This equation takes into account both residual noise and

speech distortion. Figs. 6(a)9(a) compare the SNR im-provement of various speech enhancement methods in whitenoise, Volvo engine noise, factory noise, and speechlike noisewith different noise levels. Our proposed method produces


Fig. 7. Comparison of different speech enhancement methods in Volvo enginenoise by (a) SNR improvement and (b) IS distortion.

Fig. 8. Comparison of different speech enhancement methods in factory noiseby (a) SNR improvement and (b) IS distortion.

higher SNR improvement than other methods, particularly forlow-input SNRs. The best noise reduction is obtained in thecase of white Gaussian noise, while for colored noise theimprovement is less prominent.

It has been shown by experiments that even though the SNRsare very similar at the output of the enhancement system, thelistening test and speech spectrograms can produce very diver-gent results. Therefore, segmental SNR alone is not sufficientto indicate the speech quality and further objective measure isneeded to attest the performance ascendancy. IS distortion [22]provides a higher correlation with subjective results than theSNR for speech processing systems. It is derived from the linearpredictive coefficient vector s(m) of the original clean speechframe and the processed speech coefficient vector s(m) asfollows:

IS(m) = 2s(m)2s(m)

s(m)Rs(m)Ts (m)

s(m)Rs(m)Ts (m)+ log

(2s(m)2s(m)

) 1(43)

where 2s(m) and 2s(m) are the all-pole gains for the processedand clean speeches, respectively, and Rs(m) denotes the cleanspeech signal correlation matrix. The IS distortion measuregives a zero response when the distortion of two signals to

Fig. 9. Comparison of different speech enhancement methods in speechlikenoise by (a) SNR improvement and (b) IS distortion.

be estimated have equal linear predictive coefficients and gain.Smaller value of IS implies better speech quality.

Figs. 6(b)9(b) show the IS distortion of various methods indifferent noise environments at varying noise levels. All figuresshow that the proposed method outperforms other methods withsignificant margins. This is attributed to the holistic reductionof the background noise, residual noise and speech distortion.In low SNR, GPTFS can suppress most of the noise by ap-propriately tuning the subtraction parameters according to thetimefrequency masking threshold. This tradeoff control helpsto minimize the processing distortion in the enhanced speech.The USE of the proposed system compensates for the speech inthe high-frequency range. It further improves the intelligibilityand reduces the distortion. When the SNR is high, the pro-posed system has excellent performance. Our proposed systemhas successfully overcome the major drawback of traditionaldenoising methods, which is the tendency to deteriorate someuseful components of speech, resulting in the weakening of itsintelligibility.

B. Speech Spectrograms

The above objective measures do not provide informationabout how speech and noise are distributed across frequency. Inthis perspective, the speech spectrograms, which yields moreaccurate information about the residual noise and speech dis-tortion than the corresponding timing waveforms are analyzed.All the speech spectrograms presented in this section usedKaiser Window of 500 samples with an overlap of 475 samples.Experiments show that the noisy phase is not perceived aslong as the local SNR is greater than about 6 dB. However,at SNR = 0 dB, the effect of the noisy phase is audible and isperceived as an increased roughness.

The spectrograms of noisy and enhanced speeches obtainedwith the proposed method in various noise environments showthat the residual noise has been greatly reduced, as long asthe noise remains stationary or piecewise stationary. Fig. 10shows the comparisons of the speech spectrograms obtainedby different enhancement methods in speechlike noise. As thenonstationary of noise increases, the results of our proposedmethod are still better than other algorithms. This is becausethe proposed PWPT filter bank has closely approximated the


Fig. 10. Speech spectrograms. (a) Original clean speech. (b) Noisy signal (additive speechlike noise at a SNR = 0 dB). (c) Speech enhanced by B&R01 [5].(d) Speech enhanced by Li01 [14]. (e) Speech enhanced by Lu04 [16]. (f) Speech enhanced by Hu04 [12]. (g) Speech enhanced by the proposed method.

critical bands of the human auditory system. By appropriatelysegregating the speech and noise components of the noisyspeech in frequency and time, the subtraction parameters of ourproposed GPTFS method adapt well to the combined temporaland simultaneous masking threshold. The supplement of USEalso improves the performance of our proposed system in high-frequency noise. The worst results of the proposed methodare obtained with speechlike noise. This noise is particularlydifficult to handle by any method, because it has the samefrequency distribution as the long-term speech.

C. Subjective MeasurementsIn order to validate the performances of objective evalua-

tion, subjective listening tests are performed by subjecting the

speech to varying noise at SNR = 0 and 10 dB before they areprocessed by different algorithms. An informal subjective testwas performed with ten listeners. Each listener gives a scorebetween one and five to each test signal. The score representshis global perception of the residual noise, background noiseand speech distortion. The scale used for these tests correspondsto the mean opinion score (MOS) scale [7]. For each tester,the following procedure has been applied: first, the clean andnoisy speeches are played and repeated twice; second, each testsignal, which is repeated twice for each score, is played threetimes in a random order. This leads to 30 scores for each testsignal. The results are presented in Table III. The subjectivelistening tests confirm that the proposed enhancement methodproduces the highest quality speech perceived by the actualhuman listeners among the algorithms being tested.


TABLE IIICOMPARISON BETWEEN INFORMAL MOS AND PESQ SCORES

To prove the trend of the informal MOS scores matcheswell with the objective perceptual evaluation of speechquality (PESQ) measure [38], the PESQ scores are indicated inTable III. The PESQ algorithm is designed to predict the sub-jective opinion score of a degraded audio sample. PESQ returnsa score from 4.5 to 0.5, with higher score indicating betterquality. Form Table III, it is observed that the gap betweenthe enhanced speech and noisy speech scores is similar in bothMOS and PESQ scores.

VI. CONCLUSION

In this paper, a new speech enhancement system has beenproposed. It can be anatomized into several powerful process-ing techniques that exploit the physiology of human auditorysystem to recover high-quality speech from noise contaminatedspeech. The system consists of two functional stages workingcooperatively to perform perceptual timefrequency subtrac-tion by adapting the weights of the perceptual wavelet coeffi-cients. The noisy speech is first decomposed into critical bandsby perceptual wavelet transform. The temporal and spectralpsychoacoustic model of masking is developed to calculate thethreshold to be applied to GPTFS method for noise reduction.Different spectral resolutions of the wavelet representation pre-serve the energy of the critical transient components so that thebackground noises, distortion, and residual noise can be adap-tively processed by GPTFS method. The unvoiced speech isalso enhanced by a soft-thresholding scheme. The effectivenessof the proposed system to extract a clear and intelligiblespeech from various adverse noisy environments in compar-ison with other well-known methods has been demonstratedthrough both objective and subjective measurements. The per-formance robustness under varying signal-to-noise conditionsof the proposed system is attributable to the consideration ofboth the temporal and simultaneous maskings for the tuningof subtraction parameters in the proposed GPTFS. Togetherwith the USE, they make an average SNR improvement of5.5% by objective measurements, and an average intelligibilityimprovement of 8% by subjective evaluation.

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Yu Shao received the B.Eng. degree from the BeijingInstitute of Technology, Beijing, China, in 2002.He is currently working toward the Ph.D. degree atthe School of Electrical and Electronic Engineering,Nanyang Technological University, Singapore.

His research interests include speech enhance-ment, speech recognition, adaptive filters, andwavelets.

Chip-Hong Chang (S93M98SM03) receivedthe B.Eng. degree (Hons) from the National Univer-sity of Singapore, Kent Ridge, in 1989, and theM.Eng. and Ph.D. degrees from Nanyang Tech-nological University (NTU), Singapore, in 1993 and1998, respectively.

He served as Technical Consultant in industryprior to joining the School of Electrical and Elec-tronic Engineering, NTU, in 1999, where he is cur-rently an Associate Professor. He has been holdingjoint appointments at the university as Deputy Direc-

tor of the Centre for High Performance Embedded Systems since 2000, andProgram Director of the Centre for Integrated Circuits and Systems since 2003.His current research interests include low-power arithmetic circuits, constraineddriven architectures for digital signal processing, and digital watermarking forIP protection. He has published three book chapters and more than 120 researchpapers in international refereed journals and conferences.