# Hybrid Dilated and Recursive Recurrent Convolution Network for Time-Domain Speech Enhancement
## 4 Experiments
### Experimental Results
#### 4.3.2 Module Comparisons  
We then attempt to verify the effectiveness of the proposed hybrid dilated convolution module, that is, to combine conventional convolution to solve the problem of under-utilization of the local information of dilated convolution. The HDM module is compared with the full-dilated convolution module and the full-conventional convolution module for experiments to analyze the effects of different modules on speech enhancement performance. As shown in Figure 5, these two modules are very similar to HDM, as both include \(1\times 1\) convolution, feature fusion convolution and output \(1\times 1\) convolution, and residual connection, and the number of parameters of the two modules is consistent with HDM. The difference lies in the feature fusion convolution layer, where the full-dilated convolution uses two dilated convolutions and the full-conventional convolution uses two conventional convolutions.  
The network architecture of this experiment keeps the whole structure of the encoder and decoder unchanged. In the comparison of the modules, the GRU module of recursive learning is not used. Therefore, the network that uses HDM is defined as HDMNet. The network that used full-dilated convolution modules is defined as full-dilated convolution module network (FDMNet), and the dilation rate of dilated convolution in FDMNet is consistent with that in HDMNet. The network used the full-conventional convolution module network (FCMNet).  
Table 3 shows the experimental results of PESQ and STOI for three different modules under seen noise conditions. Table 4 shows the experimental results of PESQ and STOI for three different modules under unseen noise conditions. The average PESQ value is the evaluation value of the average speech quality under different signal-to-noise ratios, the average STOI value represents the evaluation value of the average speech intelligibility under different signal-to-noise ratios, and \"Avg.\" represents the three types of signals under different evaluation indicators.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Metrics** & \multicolumn{4}{c}{**PESQ**} & \multicolumn{4}{c}{**STOI**} \\ \hline
**SNR** & \(\mathbf{-5}\)** **dB** & \(\mathbf{0}\)** **dB** & \(\mathbf{5}\)** **dB** & **Avg.** & \(\mathbf{-5}\)** **dB** & \(\mathbf{0}\)** **dB** & \(\mathbf{5}\)** **dB** & **Avg.** \\ \hline Noisy & 1.537 & 1.843 & 2.083 & 1.821 & 66.40 & 77.56 & 84.92 & 76.30 \\ FCMNet & 1.832 & 2.268 & 2.528 & 2.209 & 76.45 & 86.02 & 90.50 & 84.32 \\ FDMNet & 1.959 & 2.441 & 2.755 & 2.385 & 78.46 & 87.31 & 91.56 & 85.77 \\ HDMNet & **2.122** & **2.654** & **3.013** & **2.596** & **82.03** & **89.52** & **93.09** & **88.22** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Experimental results of different modules under seen noise conditions for PESQ and STOI. BOLD indicates the best result for each case.  
Figure 5: The full-dilated convolution module and full-conventional convolution module.  
From the results in Tables 3 and 4, it can be seen that HDMNet obtained the best results, followed by FDMNet, and FCMNet was the worst. The experiment proves: (1) that the dilated convolution is very effective in end-to-end speech enhancement tasks, greatly improving the enhancement effect of the network model. (2) The use of the hybrid dilated convolution model improves the evaluation index compared with the full dilated convolution model, which shows that the HDM makes full use of the information of the adjacent points of the speech waveform without losing the local feature information of the speech, and improves the enhancement effect of the model.