Research on Speech Enhancement Algorithm of Multiresolution Cochleagram Based on Skip Connection Deep Neural Network

The speech enhancement e ﬀ ect of traditional deep learning algorithms is not ideal under low signal-to-noise ratios (SNR). Skip connections-deep neural network (Skip-DNN) improves the traditional deep neural network (DNN) by adding skip connections between each layer of the neural network to solve the degradation problem of DNN. In this paper, the Multiresolution Cochleagram (MRCG) features in the gammachirp transform domain are denoised to obtain the improved MRCG (I-MRCG). The noise reduction method adopts the Minimum Mean-Square Error Short-Time Spectral Amplitude Estimator (MMSE-STSA) and takes I-MRCG as the input feature and Skip-DNN as the training network to improve the speech enhancement e ﬀ ect of the model. This paper also proposes an improved source-to-distortion ratio (SDR) loss function. When the loss function uses the improved SDR, it will improve the performance of Skip-DNN speech enhancement model. The experiments in this paper are performed on the Edinburgh dataset. When using I-MRCG as the input feature of Skip-DNN, the average perceptual evaluation of speech quality (PESQ) is 2.9137, and the average short-time objective intelligibility (STOI) is 0.8515. Compared with MRCG as Skip-DNN input features, the improvements are 0.91% and 0.71%, respectively. When the improved SDR is used as the loss function of the speech model, the average PESQ is 2.9699 and the average STOI is 0.8547. Compared with other loss functions, the improved SDR has a better enhancement e ﬀ ect when used as the loss function of the speech enhancement model.


Introduction
As one of the core technologies in information science, speech enhancement technology is mainly used to enhance the clarity and intelligibility of speech polluted by noise. In recent years, speech enhancement has been widely used in mobile phones, smart appliances, multimedia applications, military eavesdropping, and other fields [1][2][3][4]. At the same time, speech recognition technology also needs speech enhancement technology [5]. In practical application, speech enhancement preprocessing is generally carried out in the speech processing system to improve the anti-interference ability of the system, thereby achieving more effective communication or interaction [6].
Speech enhancement methods can be divided into unsupervised and supervised learning methods. The most commonly used unsupervised learning methods are spectral subtraction and Wiener filtering [7,8]. A problem in traditional speech enhancement algorithms is that the enhanced speech often contains an artifact called "musical noise." Virag [9] incorporated the masking properties of the human auditory system into speech enhancement and proposed an algorithm that allows automatic adjustment of parameters in time and frequency, which effectively reduces "musical noise" but outputs a low SNR. Liu et al. [10] proposed an improved spread-spectrum speech enhancement algorithm. The algorithm dynamically calculates the parameters according to the masking threshold of the key frequency segment of each speech frame and improves the output SNR. Previous studies have shown that unsupervised speech enhancement has good performance in high SNR and stationary noise environments but poor performance in low SNR and nonstationary noise environments.
Supervised speech enhancement algorithms are divided into shallow model algorithms and deep model algorithms. The nonnegative matrix factorization speech enhancement algorithm of the shallow model algorithm constructs the signal base as the prior information of the enhancement stage under the premise of being independent of the pure speech and the noise. It processes the noise to obtain the enhanced speech [11]. Since the shallow model cannot extract useful features from the data automatically, the processing ability of high-dimensional data is limited, resulting in a poor speech enhancement effect. The deep model algorithm was introduced into the field of speech enhancement. Talbi and Bouhlel [12] proposed a speech enhancement method based on stationary bionic wavelet transform (SBWT) and spectral magnitude minimum mean square error (MMSE) estimation. Combined with LWT and artificial neural network, MMSE estimation of spectral amplitude is used, which has a good noise reduction effect. Mahmmod et al. [13,14] proposed a new estimator based on a combination of optimal linear and nonlinear Laplacian distribution, and the proposed estimator is based on MMSE perception. It reduces residual noise without destroying the speech signal and regenerates distorted speech components. In recent years, DNN has been widely used in speech enhancement [15]. At present, DNN speech enhancement can be roughly divided into two methods. The first is to seek the mapping between noise and pure speech spectrum [16], and the other is based on masking [17]. DNN-based speech enhancement usually produces excessively smooth speech, resulting in speech distortion and loss of intelligibility, and large DNNS take up large memory and slow training speed [18]. Kim and Shin [19] proposed to exaggerate the training target and use another DNN to estimate the exaggerated residual error in   Journal of Sensors DNN-based speech enhancement, so that the dynamic range of enhanced speech is closer to clean speech. Tan and Wang [20] proposed two compression pipelines to reduce the model size of DNN-based speech enhancement, reducing the model size without significantly reducing their enhancement performance. Tu and Zhang [21] proposed using Skip-DNN for speech enhancement and achieved a better speech enhancement effect. Wang and Bao [22] used Skip-DNN to study speech enhancement in the mel domain and achieved high speech quality and intelligibility. Cheng et al. [23] integrated the mel domain and gammatone domain and improved the performance of speech enhancement through DNN training. Compared with the mel filter bank and the gammatone filter bank, the gammachirp filter bank is more in line with the auditory characteristics of the human ears, so this paper will choose I-MRCG in the gammachirp transform domain to extract speech features. To improve the speech enhancement performance, especially the speech enhancement effect under low SNR, this paper uses the I-MRCG feature as the input of the Skip-DNN model. It compares the speech enhancement effect of Skip-DNN under different feature parameters and speech enhancement models. The STOI and PESQ evaluation scores under different SNR conditions are analyzed. This paper proposed an improved SDR loss function. By comparing the speech enhancement effect of the Skip-DNN model using different loss functions, the influence of the improved SDR loss function on the perfor-mance of Skip-DNN is analyzed, and the enhancement effect of the proposed model and the impact of the loss function in this paper are studied.

Gammachirp Filter
Model. The gammachirp filter model was first proposed by Irino and Patterson [24] based on the gammatone filter in 1997, and its time-domain expression is expressed as where a is the amplitude, n and b are used to adjust the distribution of the gamma function, f r is the center frequency of the gammachirp filter, t is the time, and ϕ is the initial phase. Since the initial phase has limited influence on the power spectrum, ϕ = 0 is generally taken. ERBð f r Þ is the equivalent rectangular bandwidth of the filter at frequency f r . c is the chirp factor, which has a linear relationship with the sound level intensity P s .
The frequency-domain function can be obtained by Fourier transform of the gammachirp time-domain function, where a is a constant, the second term is the Fourier transform of the time domain function of the gammatone filter, denoted as G T ð f Þ, and the third term is an asymmetric function, denoted as H A ð f Þ. By normalizing the amplitude, the frequency spectrum of the gammachirp filter can be expressed as The magnitude spectrum of the filter can be expressed as Among them, R i and A i are the amplitudes of the noisy speech and the pure speech, respectively, and θ i and a i are the phases of the two, respectively.
Assuming that the noise does not affect the phase, the estimated value S _ i of the pure speech can be approximately equal to the estimated value A _ i of the magnitude spectrum. According to the characteristics of the correlation between adjacent frames of the speech signal spectrum, the estimated value A _ i of the magnitude spectrum can be expressed. Then, the estimated value S _ i of the pure speech can be obtained: where Eð•Þ represents the expectation of the parameter, pð•Þ is the probability density function, pða i Þ is the probability density function of A i , and pða i , α i Þ is the probability of the amplitude-phase joint probability distribution.
Assuming that the noise is the stationary additive white Gaussian noise, then where Γð•Þ represents the gamma function, Mða, c, xÞ represents the confluence hypergeometric function, ν i = ðξ i /ð1 + ξ i ÞÞγ i , and ξ i and γ i represent the priori SNR and posteriori SNR, respectively. The I-MRCG process is shown in Figure 1 [25].
The I-MRCG acquisition process is as follows: (1) The speech signal is divided into subbands through the gammachirp filter bank, and cochlear images of different resolutions are obtained through different frame lengths. The frame length and frame shift are set to 20 ms and 10 ms, respectively, and then, the      (2) The low-resolution cochleagram CG2 acquisition process is roughly the same as CG1, except that the frame length is 200 ms (3) The cochlear spectrogram CG1 ′ is obtained by obtaining CG1, but the speech signal at this time is processed by MMSE-STSA noise reduction, and CG1 ′ is passed through an 11 × 11 mean filter to get CG3 (4) The cochlear spectrogram CG2 ′ is obtained by obtaining CG2, but the speech signal at this time is processed by MMSE-STSA noise reduction, and CG2 ′ is passed through an 23 × 23 mean filter to get CG4 (5) The four features are spliced together to obtain I-MRCG

Skip-DNN Speech Enhancement
Model. The skip connection is a commonly used connection form in neural networks. The traditional DNN causes network degradation due to the same weight, resulting in the poor fitting effect of complex features. The skip connection is used to break the symmetry of the network and find some useful features that are masked during the training process. The skip connection can solve the problem of singularity and gradient disappearance caused by the unidentifiable part of the model. It can also solve the problem of loss of detailed information in the transmission process due to different dimensions between layers. The missing information is supplemented by skip connections. The network structure of Skip-DNN is shown in Figure 2.
As can be seen from Figure 2, to prevent the mismatch between the dimensions of the input layer and the hidden layer in the process of skip connection, the number of nodes in some hidden layers is set as the dimension of the input layer. Because the input layer is a one-dimensional vector and the input of the Skip-DNN speech enhancement model  11 Journal of Sensors is two dimensions of time and frequency, speech and noise have strong correlations in both dimensions. Therefore, the speech feature as the network input should include context information. That is, the input speech feature parameters should include this frame and its preceding and following frames.
To illustrate the impact of skip connections on the data transmission process, the residual learning unit is shown in Figure 3.
Assume that the input speech signal feature is Y, the feature learned by the Skip-DNN is denoted as IðYÞ, and the feature obtained after Y which is linearly transformed is denoted as FðYÞ. Through the connection of Skip-DNN in Figure 3, the structure can be concluded that IðYÞ = FðYÞ + Y. In the residual network, because the network is deep, there will be redundant layers, but in Skip-DNN, the number of network layers is not deep, so there will be no redundancy layer. That is, FðYÞ is not equal to 0. The method of skip connection enables a certain gradient to be guaranteed when updating parameters in the process of backward propagation, thus solving the problem of gradient disappearance in deep networks.
This paper uses the gammachirp filter bank that can simulate the auditory characteristics of the human ear to divide the frequency domain speech into subbands and obtain multiresolution cochlear features according to different frames. Taking the ideal ratio mask (IRM) as the training target, the ratio of pure speech to noise energy is calculated. The nonlinear relationship between the feature parameters and the training target is established, and the speech enhancement model based on Skip-DNN is constructed. The model is shown in Figure 4.
In the training stage, firstly, the multiresolution cochlear feature Yðt, f Þ is obtained by subbanding the noisy speech YðtÞ by the gammachirp filter. The specific extraction process is given in Section 2.2.
Secondly, the speech and noise are converted to the time-frequency domain by the gammachirp filter and framing operation, respectively, expressed as Sðt, f Þ and Nðt, f Þ. As the training target of the speech enhancement model in this chapter, IRM calculates the ratio of pure speech and noise energy to obtain IRMðt, f Þ, which can be expressed as Among them, S 2 ðt, f Þ and N 2 ðt, f Þ represent the pure speech energy and noise energy in the time-frequency domain, respectively.
Finally, the useful speech information is extracted autonomously by Skip-DNN; the nonlinear relationship between the feature parameters and the training target and the speech enhancement model is obtained.
The noisy speech Y e ðtÞ is converted to the timefrequency domain to obtain Y e ðt, f Þ, the feature parameters are extracted, and the training target IRM e is estimated through the speech enhancement model obtained by training. The target speech spectrum can be obtained by multi-plying it by the noisy speech spectrum. Then, the estimated pure speech signal amplitude and the phase of the noisy speech are reconstructed to obtain the estimated speech, which can be expressed as Among them, S

Improved SDR Loss Function.
Mean square error (MSE) loss function is the most used in deep learning speech enhancement models [26]. Although MSE is used in many models, MSE simply calculates the similarity between a given target and an estimated target and cannot guarantee the optimal result. The small value of the model training results cannot indicate that the speech enhancement model estimates the high quality of speech. Therefore, in 2017, Venkataramani et al. [27] proposed an SDR loss function suitable for speech enhancement. The loss function SDR is obtained by calculating the ratio of the speech signal to the distorted signal, which is highly correlated with the speech quality.
The SDR loss function is shown in max y _ SDR loss y, y where y is the actual value and y _ is the predicted value.
Since it is a constant relative to the network output, its optimized negative reciprocal is expressed as loss Ven y, y It was further improved by Choi et al. [28]. The optimized loss function is shown in The value range of the loss function is between ½0,−1. This paper takes the negative value of the simplified result formula and then takes the negative logarithm, which can 12 Journal of Sensors be expressed as I-loss SDR y, y _ = − log 10 −loss SDR y, y At this time, the value range of the improved loss function (equation (13) is ½∞, 0, which is convenient to observe the change of loss in the iterative process. At the same time, by observing the logarithmic curve, we can see that the closer the logarithmic loss value is to 0, the more stable it is. Therefore, this paper chooses equation (13) as the loss function for network training.

Results
3.1. Experimental Parameter Settings. The experimental pure speech data comes from the Edinburgh dataset [29], and the noise data comes from the NoiseX-92 database. During the experiment, 70 pure speech samples of the Edinburgh dataset were used as the training set, 30 pure speech samples were used as the test set, and four kinds of noises (m109, pink, Volvo, and leopard) were used. All clean speech is mixed with the above four kinds of noise at 3 SNR levels (-6 dB, 0 dB, and 6 dB) to build a multicondition stereo database. As for signal analysis, all clean and noisy waveforms are resampled to 8 kHz. A total of 1200 noisy speeches (about 6000 s) are constructed, of which 840 are used as training data, and the remaining 360 are used as test data.
The parameter settings of the neural network: the number of iterations is 60, and the stochastic gradient descent algorithm is selected to improve the training process of the network. The number of hidden layer nodes is set to 1024, and the dropout rate is 0:2. Since ReLU helps solve the convergence problem of deep neural networks, ReLU is used as the activation function in this experiment. The voice feature of the input layer is set to 3 frames, and the voice feature of the output layer is set to 1 frame. In the processing of the following experimental data, both the speech signal and the noise signal are selected according to the above criteria.
In this paper, m109, pink, Volvo, and leopard are introduced into the pure speech signal as background noise. Among them, Section 3.2 analyzes the speech enhancement effect of noisy speech signals under different signal-to-noise ratios, different noise environments, and different models, and the evaluation results are the evaluation scores of each noise environment. Section 3.3 analyzes the speech enhancement effects under different SNRs, different noise environments, and different loss functions.

Comparison between Different Speech Enhancement
Models. This experiment trains five kinds of speech enhancement models under the condition of the SNR which is -6 dB, 0 dB, and 6 dB, namely, MRCG and DNN combination, IMRCG and DNN combination, MRCG and Skip-DNN combination, MFCC [30] and Skip-DNN combination, and I-MRCG and Skip-DNN combination. The noise in the test phase is m109, pink, Volvo, and leopard noise environment. The evaluation indicators are STOI and PESQ. The STOI and PESQ score is shown in Figure 5. To illustrate the results more clearly, the standard deviations of STOI for different models in different environments are shown in Table 1. The standard deviations of PESQ for different models in different environments are shown in Table 2.
It can be seen from Table 1 that the STOI of the speech enhancement model combined with Skip-DNN and I-MRCG for the four kinds of noise is higher than other models. It can be seen from Table 2 that the PESQ of the speech enhancement model of MRCG and Skip-DNN is slightly higher than that of Skip-DNN and I-MRCG in the Volvo noise environment, and the PESQ of the speech enhancement model of Skip-DNN and I-MRCG in the other noise environment is higher than others. It can be seen from Figure 5 that I-MRCG and Skip-DNN speech enhancement models have better effects on processing pink noise under the environment of low SNR. STOI is 7.2%, 4.4%, 2.8%, and 0.7% higher than MRCG and DNN combination, I-MRCG and DNN combination, MRCG and Skip-DNN combination, and MFCC and Skip-DNN combination, respectively. PESQ is 15.6%, 8.8%, 7.6%, and 2.4% higher than other models, respectively. For other noisy environments, the speech enhancement models of I-MRCG and Skip-DNN are also improved compared with other models.

Comparison between Different Loss Functions.
To analyze the influence of different loss functions on Skip-DNN, in the speech enhancement model based on Skip-DNN, the performances of MSE, SDR, and improved SDR three loss functions under different SNR and different background noise environments were compared, with the PESQ and STOI as performance indicators. The results are shown in Figure 6.
As shown in Figure 6, only when the background noise is Volvo and the SNR is -6 dB, the combined Skip-DNN and improved SDR speech enhancement model STOI is lower than the Skip-DNN and MSE combined model. The speech enhancement model PESQ combined with Skip-DNN and improved SDR is higher than other models.

Conclusions
This paper proposes an I-MRCG speech feature processed by MMSE-STSA. The low-resolution features after noise reduction of MMSE-STSA are spliced with the highresolution features of traditional MRCG. The obtained I-MRCG has not only detailed local information but also clear global information. The network uses Skip-DNN training and solves the problem of gradient disappearance in the training process through skip connections. During the training process, the loss function adopts SDR. It optimizes by taking the negative value and the negative logarithm, resulting in an improved SDR loss function.
The experiment compares the performance of the Skip-DNN speech enhancement model with MRCG, MFCC, and I-MRCG. The combination of Skip-DNN and I-MRCG achieves the best effect. For the pink noise environment with SNR of -6 dB, the speech enhancement effect based on Skip-DNN and I-MRCG is greatly improved, and STOI score is 0.712 and PESQ score is 2.0102. By comparing the loss functions of MSE, SDR, and improved SDR, it is