# Hybrid Dilated and Recursive Recurrent Convolution Network for Time-Domain Speech Enhancement
## 4 Experiments
### Experimental Results  
#### 4.3.1 Compared with Typical Algorithms  
In order to verify the effectiveness of the proposed speech enhancement network model RRSENet, we compared three typical speech enhancement algorithms, namely LogMMSE [44], TCNN [16], and AECNN [45]. Among them, LogMMSE is the minimum mean square error logarithmic spectrum amplitude estimation, which is a speech enhancement algorithm based on statistical models. TCNN is a speech enhancement model based on a temporal convolution neural network. The overall framework of the model consists of an encoder and a decoder, and 18 temporal convolution modules are embedded between the encoder and decoder. Compared with TCNN, RLSENet replaces the temporal convolution module used in TCNN with a hybrid dilated convolution module. While AECNN is a typical 1-D convolution encoder-decoder framework, it still needs to train a large number of parameters. The frame length of model input and output is 2048, and the number of channels in successive layers is 1, 64, 64, 64, 128, 128, 128, 256, 256, 512, 512, 256, 256, 128, 128, 128, and 1, the size of the convolution kernel of each layer is 11, and the activation function uses PReLU. RRSENet adds the GRU module on the basis of RLSENet. The experiment was tested on the matched test set and the unmatched test set. Table 1 is the comparison result of the three typical algorithms of LogMMSE [44], TCNN [16], and AECN [45] under noise matching at \(-\)5 dB, 0 dB, and 5 dB. The evaluation index is the average PESQ [46] and STOI [47] values. The \"PESQ\" value is the mean of speech quality under different signal-to-noise ratios in case of matched noise. The \"STOI\" value is the mean of speech intelligibility under different signal-to-noise ratios. The average PESQ value is the average speech quality evaluation value 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 the \"Avg.\" represents the three types of signals under different evaluation indicators. HDMNet is a network structure that does not use GRU modules; RLSENet is a recursive learning network using the HDM modules; and RRSENet is a network structure that uses HDM modules and GRU modules. The results in the Table 1 show that the RLSENet and RRSENet using recursive learning network outperform the other three speech enhancement algorithms on PESQ and STOI evaluation metrics. Among them, \"HDMNet\" is the speech enhancement network that uses only the HDM module. The traditional method LogMMSE enhancement is the least effective, indicating that it is difficult to handle non-smooth noise. In contrast to the temporal convolution module used in TCNN, which only considers the historical information and uses a one-dimensional dilated convolution with its own defects, the hybrid dilated module proposed in this paper is better than the traditional convolution block, making full use of the information of the neighboring points of the speech waveform without losing local information and improving the enhancement performance of the model. Compared with RLSENet, RRSENet adds a GRU module, which makes the results of RRSENet better than RLSENet. In general, comparing with other network models, the RRSENet network model proposed in this paper has the best performance. For example, in a low SNR-5 dB noise environment, the enhanced speech with RRSENet network model achieves the best enhancement performance compared to the unprocessed noisy speech with PESQ and STOI by 0.693 and 16.92%, respectively. The AECNN and the TCNN using the temporal convolution module are slightly inferior, which proves that the RRSENet network model is more suitable for end-to-end speech enhancement tasks. From the results in Table 2, it can be seen that at a low signal-to-noise ratio of \(-5\) dB, the enhanced speech of RRSENet has increased by 4.5% and 4.98% compared with the enhanced speech of TCNN and AECNN, respectively.