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Speech intelligibility prediction with the dynamic compressive gammachirp ﬁlterbank and modulation power spectrum

: The speech-based envelope power spectrum model (sEPSM) was developed to predict the speech intelligibility of sounds produced by nonlinear speech enhancement algorithms such as spectral subtraction. It is a linear model with a linear, level-independent gammatone (GT) ﬁlterbank as the front-end. Therefore, it seems diﬃcult to evaluate speech sounds with low and high sound pressure levels (SPLs) consistently because the intelligibility of the speech is dependent on the SPL as well as the signal-to-noise ratio. In this study, the sEPSM was extended with the dynamic compressive gammachirp (dcGC) auditory ﬁlterbank and a ‘‘common’’ normalization factor of the modulation power spectrum component to improve the predictability of the model. For evaluating the proposed model, we performed subjective experiments on the intelligibility of speech sounds enhanced by spectral subtraction and a Wiener ﬁlter algorithm. We compared the subjective speech intelligibility scores with the objective scores predicted by the proposed dcGC-sEPSM, original GT-sEPSM, and other well-known conventional methods such as the short-time objective intelligibility measure (STOI), coherence speech intelligibility index (CSII), and hearing aid speech perception index (HASPI). The result shows that the proposed dcGC-sEPSM predicted the subjective results better did than the other methods.


INTRODUCTION
It is important to develop objective intelligibility and quality measures for assistive listening devices including hearing aids (HAs) [1]. Although many noise reduction or speech enhancement techniques have been developed, it is still necessary to perform human listening tests for evaluating assistive listening devices as a de facto standard of objective measure is not available. Standard objective measures such as speech intelligibility index (SII) and speech transmission index developed for linear trans-mission lines cannot account for the nonlinear processes involved in speech enhancement algorithms, as in the SII extended for hearing impaired (HI) listeners [2]. As recent assistive devices use nonlinear speech enhancement techniques, objective measures should be developed for both normal hearing (NH) and HI listeners. Moreover, it is also desirable that an objective measure can accommodate individual differences in hearing loss.
A promising strategy for developing such objective measures is the introduction of auditory models based on psychoacoustic and physiological knowledge. Several models have been proposed to predict speech intelligibility for NH listeners. The spectro-temporal modulation index [3] is based on the gammatone auditory filterbank and a two-dimensional spectro-temporal modulation filterbank, and it accounts for the speech intelligibility of phasejittered speech. The speech-based envelope power spec-trum model (sEPSM) [4] uses a time-domain modulation filter to account for the intelligibility of speech sounds enhanced by spectral subtraction. The two-dimensional sEPSM (2D-sEPSM) [5] combines both methods and possesses the advantages of both. These models are successful under their evaluation conditions. However, they are restricted to speech intelligibility for NH listeners at moderate sound-pressure levels (SPLs) because the linear gammatone filterbank cannot account for the leveldependent frequency selectivity and gain of cochlear filtering and for the gain losses in HI listeners [6]. It is well known that speech intelligibility decreases as the signal level decreases and that filter characteristics change depending on the signal level; therefore, it is not suitable to use the linear filter defined at moderate SPLs. Recently, the hearing aid speech perception index (HASPI) [7] was proposed for speech intelligibility for both HI and NH listeners by introducing a nonlinear gain with gammatone filters to overcome some of the problems faced in speech perception. However, this filter system with the gammatone cannot well account for realistic psychoacoustic data, as described in the next section.

Toward Prediction Model for Both NH and HI
One of the most crucial issues when developing such auditory-based prediction models is whether the parameters for the auditory characteristics can be estimated precisely from psychoacoustic experiments performed with both NH and HI listeners. In particular, it is important to account for threshold data derived by a notched-noise (NN) masking experiment, which is the de facto standard method for estimating the frequency characteristics of auditory filters [6]. The gammachirp (GC) filter was proposed as an extension of the gammatone filter to account for the leveldependent characteristics derived from psychoacoustic and physiological experiments [8]. The GC filter is a cascade of a linear passive gammachirp filter (pGC) and a leveldependent, high-pass asymmetric filter (HP-AF). The signal level, which is estimated from the output of the pGC, controls the center frequency of the HP-AF. The gain of the HP-AF changes in accordance with the center frequency, and the gain of the linear pGC is constant. This structure enables the GC filter to simulate a level-dependent auditory filter [8]. It was demonstrated that the GC filter explains NN masking data well for both NH and HI listeners [9,10].
In contrast, gammatone filters and their extensions used in prediction models have never been fitted directly to NN masking data. Moreover, they do not seem to account for the masking data successfully, as the frequency response is symmetric or nearly symmetric with respect to the linear frequency axis. To the best of our knowledge, only two time-domain auditory filters were directly fitted to NN masking data: GC and pole-zero filter cascade model [11]. Therefore, the introduction of the GC filter estimated for an individual NH or HI listener would improve the speech intelligibility prediction.

Prediction Model with dcGC Filterbank
The dynamic compressive gammachirp filterbank (dcGC-FB) [12] was proposed to simulate frequency analysis in the cochlea. Yamamoto et al. [13] extended sEPSM by using dcGC-FB (dcGC-sEPSM) to improve the speech intelligibility prediction of signals enhanced by the state-of-the-art Wiener filter (WF) with a pretrained speech model (PSM) described in Sect. 3.1.2. One study reported that dcGC-sEPSM predicts the speech intelligibility better than do coherence SII (CSII) [14] and shorttime objective intelligibility (STOI) techniques [15], which have recently become popular as objective speech intelligibility measures. However, it was also found that the original dcGC-sEPSM failed to predict speech intelligibility for some conditions. For example, the prediction is smaller for the WF (WF 0:0 PSM ) than for the spectral subtraction (SS 1:0 ), as shown in Fig. 2(b) of [13]. This is inconsistent with the subjective result. Because this is a common tendency with the original sEPSM, there might be an inherent problem.

Extension of dcGC-sEPSM
We extended dcGC-sEPSM to resolve the problem by introducing a common denominator in power normalization, as described in Sects. 2.2.1 and 4.2.3. Moreover, we use more reliable statistics, such as a Bland-Altman analysis [16,17], to compare its performance with that of other methods, including HASPI, in Sect. 4.2.2. Our goal is to develop an objective intelligibility measure for both NH and HI listeners based on an accurate estimate of the auditory filter characteristics. In this study, we have performed an evaluation by using NH listener data as the first step.

OVERVIEW OF dcGC-sEPSM
Cochlear signal analysis is modeled using a bank of auditory filters. The frequency selectivity and gain of the auditory filter are level dependent. Irino and Patterson [12] proposed the dynamic compressive gammachirp filterbank (dcGC-FB) to account for the psychophysical and physiological data with level-dependent characteristics [8,18]. The dcGC-FB is much more advantageous for simulating auditory peripheral processing than the linear gammatone auditory filterbank (GT-FB). It is worth replacing the GT-FB in the original sEPSM with the dcGC-FB to better predict the speech intelligibility of various speech enhancement techniques. Figure 1(a) shows a block diagram of the sEPSM extended using the dcGC-FB, which is called the ''dcGC-sEPSM.'' The following is the main difference between the dcGC-FB and the original sEPSM [4], hereafter referred to as the ''GT-sEPSM,'' that uses a gammatone filterbank (GT-FB). The dcGC-sEPSM uses 100-ch dcGC filters that are equally spaced on the ERB N number, and they cover a speech range of 100-6,000 Hz [12]. The dcGC filter represents the level-dependent filter characteristics of an average NH listener [9] in the current version, and it can be extended to represent those of HI listeners. In contrast, the GT-FB in the GT-sEPSM only has a sparse set of filters, specifically, 22 channels in the range of 63-8,000 Hz, to reduce the redundancy with respect to frequency overlap between adjacent filters [4]. Thus, it cannot well characterize the frequency analysis of HI listeners who have wider auditory filters [6].

Calculation of SNR in Envelope Domain
In the sEPSM, the temporal envelope is extracted from the output of an individual auditory filter by using a Hilbert transform and a low-pass filter with a cutoff frequency of 150 Hz. The power spectrum of the temporal envelope, S env , is calculated using fast Fourier transform (FFT). The modulation spectrum is calculated in the modulation frequency domain, f env .

Calculation of envelope power
If the power spectrum of the j-th modulation filter at a center frequency, f c ð jÞ, is denoted as W f c ð jÞ ð f env Þ, the modulation power spectra are calculated for an enhanced speech sound, P env;Ŝ , and an estimated residual noise, P env;Ñ , as where the asterisk (Ã) represents eitherŜ orÑ, and S env;Ŝ ð0Þ represents the 0-th order coefficient of the FFT, that is, the DC component of the modulation power spectrum ofŜ. Note that the calculation of P env;Ñ has been modified from that of the GT-sEPSM [4] and the previous dcGC-sEPSM [13] to improve the predictability, as described in the next The total number of modulation power spectra, P env , is 700, which is the product of the number of auditory filter channels, ifij1 i 100g, and the number of modulation filter channels, jf jj1 j 7g.Ŝ andÑ are the outputs of the noise reduction algorithm.Ŝ is the enhanced speech signal andÑ is the estimated noise residue, as shown in Fig. 1(b). When the noise reduction algorithm is not applied (i.e., ''unprocessed'' condition),Ŝ is the same as noisy speech, S þ N, andÑ is the same as additive noise, N.

Difference from previous models
In the original GT-sEPSM [4] and the previously reported dcGC-sEPSM [13], the normalization denominators were S env;Ŝ ð0Þ and S env;Ñ ð0Þ when calculating P env;Ŝ and P env;Ñ , respectively. This means that the modulation power spectra are individually normalized by the DC component of the same source. The use of ''individual'' denominators may cause prediction errors because the efficiency of noise reduction cannot be reflected in P env;Ñ . The power, P env;Ñ , is a result of normalization by S env;Ñ ð0Þ, and thus, it tends to remain constant even when S env;Ñ ð0Þ is effectively reduced by a good algorithm. Equation (1) resolves this problem by using a single, ''common'' denominator, S env;Ŝ ð0Þ. It is an important change to improve the prediction. Section 4.2.3 discusses the effects of individual and common denominators on predictions.

Calculation of SNR
The signal-to-noise ratio (SNR) in the modulation frequency domain, SNR env , is calculated from the modulation power spectra of the enhanced speech, P env;Ŝ , and the noise residue, P env;Ñ . The individual SNR env; j for the j-th modulation filter is defined as the ratio of the powers summarized across the auditory filter channel, i, and it is given as The total SNR env is calculated as In contrast, SNR env in the original GT-sEPSM [4] was calculated as where the auditory filter channel is ifij1 i 22g, and the modulation filter channel is jf jj1 j 7g.

Transformation from SNR env to Percent Correct
Value Speech intelligibility as a percent correct value, P correct , is estimated from SNR env . First, the sensitivity index, d 0 , of an ''ideal observer'' is calculated from SNR env . Then, P correct is estimated from d 0 using a multiple-alternative forced choice (mAFC) model [19] in combination with an unequal-variance Gaussian model as follows: where Note that È denotes a cumulative normal distribution, and k and q are empirically determined constants. The values of " N and ' N are determined by the response-set size, m, of the mAFC. ' S is related to the redundancy in the speech material (e.g., sentences or monosyllables) as described in Appendix A.

MODEL EVALUATION
The dcGC-sEPSM was compared with recent speech intelligibility models using enhanced speech sounds.

Speech Enhancement Algorithms
In this study, we used two popular single-channel speech enhancement techniques for evaluation: spectral subtraction (SS) [20], which was used in the original sEPSM study [4] and by us for the purpose of comparison, and WF, which is widely used to obtain a final result of enhanced speech after estimating the speech and noise spectral densities through many state-of-the-art approaches including a vector Taylor series based model [21], nonnegative matrix factorization [22], and deep neural network [23].

Spectral subtraction
We estimated the amplitude spectrum of clean speech, Sð f Þ, by using SS [20], which was defined as whereP N ð f Þ represents the noise power spectrum (N) estimated from a nonspeech segment and P SþN ð f Þ is the power spectrum of noisy speech (S þ N). The parameter denotes the over-subtraction factor ( 0). denotes the spectral flooring parameter (0 < ( 1). We calculated the power and phase spectra using a short-time Fourier transform with a 1,024-point Hanning window and a 50% frame shift at a sampling frequency of 16 kHz.

Wiener filter with pretrained speech model
The WF used in this study was estimated using a PSM [21,24]. This method is referred to as WF PSM below. The PSM is defined as a Gaussian mixture model that is defined in the Mel-spectrum domain using a vector Taylor-seriesbased model combination algorithm. This algorithm can estimate the speech component of noisy speech based on the PSM, which represents the statistical distribution of the spectral features in clean speech after training with a large speech database consisting of more than 30,000 sentences spoken by 180 speakers. In this evaluation, we used the PSM with a 24-channel Mel-filterbank and set the number of Gaussian mixture components for speech and noise at 64 and 1, respectively. The WF gain applied to the noisy speech in the linear frequency domain was calculated using frequency warping from the Mel-frequency domain.

Subjective Experiments
We performed speech intelligibility experiments using Japanese four-mora word speech sounds obtained from a database (FW07) [25,26]. The speech sounds of a male (speaker label: ''mis'') were obtained from the lowest familiarity set, thereby preventing the listeners from guessing the speech sounds. We prepared nine noisy speech sets as follows, such that every subject had to listen to a different set to balance the word difficulty.

Production of noisy sound and enhancement
Noisy speech sounds at SNRs of À6, À3, 0, and 3 dB were generated by mixing clean speech sounds and pink noise, where the noise level was kept constant and the speech level was changed in accordance with the SNR. This is the same procedure as that used in experiments with the FW07 database [26]. These sounds are hereafter referred to as ''unprocessed'' sounds. We generated enhanced speech sounds using the SS in Sect. 3.1.1 and the WF PSM in Sect. 3.1.2. The over-subtraction factor, , for the SS was fixed at 1.0 as a reference condition for comparisons with the results in [4]. This method is hereafter referred to as ''SS ð1:0Þ .'' In WF PSM , it is possible to control the amount of residual noise with the parameter "f"j0 " 1g of the Wiener gain shown in Eq. (18) of [24]. The residual noise increases as the value of " increases. We used WF PSM with " values of 0, 0.1, and 0.2, referred to as ''WF ð0:0Þ PSM ,'' ''WF ð0:1Þ PSM ,'' and ''WF ð0:2Þ PSM ,'' respectively. Note that the enhancements described above were performed at the sampling frequency of 16 kHz owing to the limit of the program for the WF PSM .

Sound presentation
The sounds were presented diotically via a DA converter (Fostex, HP-A8) over headphones (Sennheiser, HD-580) at a quantization of 24 bit and a sampling frequency of 48 kHz after up-sampling from 16 kHz. The level of stimulus sounds was 65 dB in L Aeq . Listeners were seated in a sound-attenuated room with a background level of approximately 26 dB in L Aeq .

Listeners and task
Nine (four male and five female) NH listeners aged between 20 and 23 participated in the experiments after providing informed consent. We confirmed that all listeners had hearing loss of less than 20 dB in the range of 125-8,000 Hz and that their native language was Japanese. The listeners were instructed to write down the words that they heard using ''hiragana,'' which roughly corresponds to Japanese morae or CV syllables. The total number of presented stimuli was 400 words consisting of a combination of five signal processing conditions (''unprocessed,'' ''SS ð1:0Þ ,'' ''WF ð0:0Þ PSM ,'' ''WF ð0:1Þ PSM ,'' and ''WF ð0:2Þ PSM '') and four SNR conditions (À6, À3, 0, and 3 dB SNR) with 20 words per condition. Note that the words for each condition corresponded to a set of 20 words in FW07. The assignment of a word set to a condition was randomized across listeners to avoid bias owing to the variability in the word difficulty experienced by each listener. Thus, the total number of word sounds was 3,600 (= 400 words Â 9 listeners). The percentage of correctly identified words was used for comparisons.

Speech Intelligibility Models
We compared the proposed model with the original sESPM and recent models including STOI [15], CSII [14], and HASPI [7]; these are relevant to the evaluation of nonlinear speech enhancement algorithms and are frequently cited in related papers [1,27].
We calculated the speech intelligibility from the same speech sounds, that is, the 3,600 words, used in the subjective experiments. Therefore, the model predictions were derived for the word sets provided to the individual listeners. In the following prediction models, several parameters need to be tuned depending on the speech material used in the evaluation. This is also the case in the previous papers cited above. In this study, for a fair comparison, the parameter values were determined by a least mean squares method such that the model predictions matched the intelligibility scores of human subjects for the ''unprocessed'' sounds. The capabilities of the models to predict speech intelligibility based on the individual speech enhancement algorithms were investigated.

GT-sEPSM and dcGC-sEPSM
In the GT-sEPSM and dcGC-sEPSM, the values of the four parameters k, q, ' S , and m in Eqs. (5) and (6) need to be determined. We fixed q ¼ 0:5, as described in [4], and m ¼ 20;000, as described in [13]. k and ' S were determined to minimize the mean-squared error of the ''unprocessed'' curves between the human result and the model prediction, as described above. The results were k ¼ 1:62 and ' S ¼ 2:70 for the dcGC-sEPSM and k ¼ 0:40 and ' S ¼ 2:85 for the GT-sEPSM.

STOI
Recently, the STOI [15] has become a popular measure for the evaluation of speech enhancement algorithms. It consists of a one-third octave band filterbank, envelope extraction, and normalization to calculate the correlationbased intelligibility measure d, as described in [15]. The speech intelligibility in percentage is derived using a logistic function SI ¼ 100=f1 þ expðad þ bÞg as in Eq. (8) of [15]. The optimized parameter values for our condition were a ¼ À6:44 and b ¼ 4:56.

CSII and HASPI
The CSII [14] is an extension of the SII standard using roex auditory filters [6] and a magnitude-squared coherence (MSC) function, which is the cross-spectral density of enhanced speech and clean speech.
The HASPI is a recent version developed to predict speech intelligibility for HI listeners using an extended version of the gammatone filterbank. This index is calculated from the normalized cross-correlation of the temporal sequence of the cepstral coefficients in addition to the coherence values, similar to the MSC used in the CSII. The input level of HASPI needs to be adjusted as described in Appendix because it is a level-dependent model.

RESULTS
The performance of the proposed model was evaluated through comparisons between the human subjective results and the predictions by the proposed model and other models. Figure 2 shows the percent correct values of word recognition as a function of the speech SNR in the human subjective experiments. The percent correct value increases as the SNR increases, and the standard deviations were approximately 10 percentage points. The effects of the SNRs and speech enhancement algorithms on the averaged intelligibilities were assessed using a two-way analysis of variance (ANOVA). The result showed that the main effect of the SNRs was significant (Fð3; 160Þ ¼ 131:78, p < 0:0001), the main effect of speech enhancement algorithms was also significant (Fð4; 160Þ ¼ 10:17, p < 0:0001), and the interaction was not significant (Fð12; 160Þ ¼ 1:20, p ¼ 0:29). A post-hoc multiple-comparison analysis (Tukey-Kramer HSD test, ¼ 0:05) indicated that the speech intelligibility scores of the enhanced speech processed by SS ð1:0Þ were significantly lower than those of the unprocessed speech. There were no significant differences between the other algorithms and the unprocessed speech. Figure 3 shows the model predictions in the same format as that used for the human results in Fig. 2. Figure 3(a) shows the results of the proposed dcGC-sEPSM with the common denominator, S env;Ŝ ð0Þ, in Eq. (1). Figure 3(b) shows the results of the dcGC-sEPSM when the power normalization was performed by using the individual denominator as in [4,13]. Note that the model predictions in this panel are different from the curves shown in Fig. 2(b) in the previous report [13], in which there were errors in the noise estimate. The parameters of Eq. (5) in this panel are k ¼ 1:99 and ' S ¼ 2:17; these are different from the previous ones. This model is hereafter referred to as ''dcGC-sEPSM (indiv. denom.).'' It is clear that the common denominator in the proposed dcGC-sEPSM improves the predictions of WF PSM s. Figure 3(c)  Table 1 summarizes the RMS difference in the percent correct values between the human result and the model prediction. The total RMS difference of the dcGC-sEPSM is the smallest in all prediction models. The total RMS of the GT-sEPSM is the largest. The result also shows that the common denominator in Eq. (1) improves the predictions because the total RMS of the dcGC-sEPSM is smaller than that of the dcGC-sEPSM (indiv. denom.).

Model Evaluation
For individual enhancement algorithms, the dcGC-sEPSM gives the smallest values for WF 0:1 PSM and WF 0:2 PSM . The CSII gives the smallest values for WF 0:2 PSM and WF 0:0 PSM but gives the largest values for SS 1:0 . The STOI gives the smallest values for SS 1:0 but relatively large values for WF PSM .

Bland-Altman analysis
A correlation analysis is commonly used in model evaluations [27]. It is suitable for evaluating the similarity between two sets of data but not the difference. In this study, the difference was analyzed using a Bland-Altman analysis [16,17].
For a pair of data vectors A and B, the Bland-Altman plot is a scatter plot in which the ordinate represents the difference between the two paired data (A À B) and the abscissa represents the average (ðA þ BÞ=2). The plot enables an analysis of the difference in two potential sources of systematic difference: fixed and proportional bias. A fixed bias implies that a model predicts values that are higher (or lower) than those obtained from a human by a constant number. A proportional bias implies that a model predicts values that are higher (or lower) than those obtained from a human by a number that is proportional to the level of the measured variable (SNR). It is possible to test whether the bias is significantly different from zero. Table 2(a) summarizes the fixed bias between the human results and the model predictions based on the Bland-Altman plot (figures are not presented here). The model is better as the fixed bias is closer to zero. Only five combinations give nearly zero bias (no significance). Other combinations give bias values significantly different from zero. The minimum fixed biases were given by the dcGC-sEPSM with WF 0:1 PSM , the CSII with WF 0:0 PSM and WF 0:2 PSM , and the STOI with SS 1:0 . The fixed biases (in absolute values) of the dcGC-sEPSM with WF 0:0 PSM are smaller than 10 percentage points and are the second best, whereas the fixed biases of the dcGC-sEPSM (indiv. denom.), STOI, and HASPI with WF 0:0 PSM and WF 0:1 PSM are larger than 10 percentage points. The fixed bias of the CSII with SS 1:0 is larger than 20 percentage points. In summary, the dcGC-sEPSM generally gives smaller fixed biases than the other models. effective to introduce the nonlinear dcGC-FB and the common denominator in the normalization of the DC components in Eq. (1), at least for WF PSM . The replacement of the GT-FB with the dcGC-FB improved the performance, as shown in Figs. 3(b) and (c). This was probably because the nonlinear compression in the dcGC-FB properly compensated the level of the modulation components, which a human may use in speech perception. The common denominator also improved the performance, as shown in Figs. 3(a) and (b). The common denominator preserves the ratio between the modulation components of the reference and test sounds, whereas the individual denominator normalizes the level of the modulation component and removes the information about the ratio. This factor enables a more accurate estimation. In contrast, the individual denominator, as in [4] and [13], normalizes the level difference between these sounds. It is unrealistic, as the prediction would remain unchanged even when the levels are completely different.

Effect of filterbank
The CSII (Fig. 3(e)) did not predict the speech intelligibility for the SS 1:0 properly. This is mainly because the MSC in the CSII [14] is largely reduced by the SS because both the MSC and the SS are calculated in the Fourier spectral domain and the SS induces a large distortion in the spectrum. This is not the case for the other methods because the distortion measure is calculated after the filterbank output (i.e., the gammatone in the sEPSM and the HASPI, the one-third octave filterbank in the STOI, and the gammachirp in the dcGC-sEPSM). A filter with a wide bandwidth summarizes the spectral information across the frequencies, and this process may smear the SS distortion. As a result, the models with the filterbanks may improve the speech intelligibility prediction with the SS.

CONCLUSIONS
The sEPSM was extended using the dcGC-FB with refined power normalization. The speech intelligibility of the enhanced speech sounds was compared using the subjective results and model predictions. The results demonstrated that the dcGC-sEPSM could predict the human results for WF PSM better than could the original sEPSM, STOI, CSII, and HASPI. The STOI, which has often been used as an objective measure for speech enhancement, predicted the human results for SS 1:0 better. However, the dcGC-sEPSM seems advantageous for evaluating WF techniques that are commonly used in various speech enhancement algorithms. The use of the dcGC-FB in the prediction models is advantageous because the parameter values of the GC filter can be directly estimated from the threshold data of an NN masking experiment with NH and HI listeners.