# Speaker-Independent Spectral Enhancement for Bone-Conducted Speech
## 3 A Method of Speaker-Independent Bone-Conducted Speech Enhancement
### The GAN Model of BC Speech Enhancement  
The main problem of BC speech enhancement is the loss of high-frequency signal information and speech consonants, which requires a specific algorithm to recover the missing relevant part of speech information. However, the traditional way to infer the enhanced speech based on BC speech does not perform well in the task. With the extensive application of deep learning methods in various fields, the GAN [12] has added a binary discrimination model to improve the generation effect on the basis of a single network, which can learn high-dimensional features and complex data internal distribution, infer real samples from potential space, and can be used to generate more sample data in scenes with more missing data. Therefore, this paper uses the GAN to realize the blind enhancement task of speaker-independent BC speech. Figure 2 shows the main structure of the BSEGAN-SI method proposed in this paper. Through the power generation ability of GAN, the mapping relationship between BC and AC is established to recover part of the speech information lost by BC speech and improve the hearing quality of BC speech. According to the relevant introduction in Section 2, this paper uses the GAN to model the complex nonlinear mapping relationship between BC and AC speech signals. Figure 1: Architecture of the proposed BSEGAN-SI method. Figure 2: The structure of the GAN model in the BSEGAN-SI method. We found that the sigmoid cross-entropy loss training using the original GAN is prone to instability. The LSGAN [28] method uses the loss of least squares to replace the cross-entropy loss of the original GAN and has achieved certain results in the quality of generated information data. Thus, the adversarial loss functions of discriminator and generator loss are  
\[\mathcal{L}_{dis}^{adv}(D)=\frac{1}{2}\mathbb{E}_{\mathbf{t}\sim p_{data}(\mathbf{t})}[ (D(\mathbf{t})-a)^{2}]+\frac{1}{2}\mathbb{E}_{\mathbf{s}\sim p_{data}(\mathbf{s})}[(D(G( \mathbf{s}))-b)^{2}] \tag{7}\]  
\[\mathcal{L}_{gen}^{adv}(G)=\frac{1}{2}\mathbb{E}_{\mathbf{s}\sim p_{data}(\mathbf{s})} [(D(G(\mathbf{s}))-c)^{2}] \tag{8}\]  
where \(a=1\), \(b=0\) and \(c=1\) are fixed constants. Source BC features map \(\mathbf{s}\) and target the AC features map \(\mathbf{t}\). In the BC speech enhancement method designed in this paper, the structure of the generator model is shown in Figure 3. The encoder-decoder [17] network framework is adopted. To enable the framework to rapidly enhance BC speech, we reasonably control the complexity of the model to achieve a faster speed and achieve better results. The network of the generator and discriminator of BSEGAN-SI selects a convolutional neural network as the core network layer of the whole structure, which is a fully convolutional network. The structure of the whole generator network and deep convolution generative adversarial networks (DCGAN) [29] is consistent with discarding the pooling layer. The pooling layer operation will cause part of the information loss of the speech features. For BC enhancement, it will reduce the enhanced BC speech quality. Normalization operation is a common method proposed to simplify operation. Generally, data are mapped to a relatively small range, which can facilitate data processing. Before network training, we preprocessed the extracted speech feature data, including normalization, to reduce the large difference between data, so that the model could be better trained. The convolution layer of the generator is realized by two-dimensional (2D) convolution. Gated CNN [30] adds gated linear units (GLUs) to the model to capture long-term memory, and the number of nonlinear calculations of this structure is reduced, which can accelerate the convergence speed of the model. We all adopt this structure in the encoder-decoder module and add a GLU layer to improve the model's ability to capture speech feature information.