# Two-Stage Single-Channel Speech Enhancement with Multi-Frame Filtering
## 6 Conclusions  
In this study, a two-stage model for single-channel speech enhancement is proposed. There are two DNNs in the proposed model--in the first stage, one of the two DNNs is trained first. In the second stage, the other DNN uses the enhanced speech from the trained DNN as extra input features. To further improve the enhancement performance and reduce the distortion introduced by neural networks, the result of a single-channel filter is also used in the second stage to guide the training of the model. Two different single-channel filters are investigated in this study, namely, MFMVDR and MFWF. We investigate the influence of the number of frames used to calculate the filter and the padding mode on the performance of the two filters. We also compare the impact of MFMVDR and MFWF on the final model performance and find that MFMVDR delivers more improvement.  
Our main contribution is proposing a two-stage training approach in the single-channel scenario, which utilizes the information from MFMVDR filters to assist in neural network training. As a result, our method achieves improved speech enhancement performance and higher speech recognition accuracy. Experiments on two datasets containing both synthetic and real-world noisy speech show that the proposed model has better enhancement performance and generalization ability. On the WHAM! test set, our model exhibited a relative improvement of 3% in SI-SNR and 2% in WER compared to the best-performing baseline model, DPRNN. On the synthetic test set of CHiME-4, our model demonstrated substantial relative improvements of 40% and 20% in SI-SNR and WER, respectively. Additionally, our model exhibited a noteworthy relative improvement of 9% in WER on the more challenging real test set of CHiME-4. The ablation study demonstrates the effectiveness of the two-stage training strategy and the incorporation of MFMVDR results in training.  
Possible directions for future improvements include:
* Smaller model parameters. In this study, we employ TCN-DenseUNet, a time-frequency domain model, for both DNN\({}_{1}\) and DNN\({}_{2}\). Our future research will explore the use of time-domain models, such as DPRNN, as the structure for DNN\({}_{1}\) and DNN\({}_{2}\) to reduce the number of model parameters.
* Improved training strategies. For example, using the parameters of DNN\({}_{1}\) to initialize DNN\({}_{2}\) in the second stage, followed by fine-tuning DNN\({}_{2}\), or jointly training DNN\({}_{1}\) and DNN\({}_{2}\) with DNN\({}_{1}\) using a smaller learning rate to speed up model convergence and further improve performance.
* More refined information fusion methods. In this study, the input of DNN\({}_{2}\) is a simple concatenation of \(\hat{X}^{(1)}\), \(\hat{X}^{(F)}\), and \(Y\). In future research, more sophisticated methods can be explored to fuse the information of the three, such as attention mechanisms.
* Diversified model selection. We could make DNN1 or DNN2 a time-frequency domain model, and the other a time-domain model. It is hoped that these two models can complement each other to achieve better enhancement performance.  
Conceptualization, W.Z. and S.L.; methodology, W.Z. and S.L.; software, W.Z. and S.L.; validation, S.L., W.Z. and Y.Q.; investigation, S.L.; resources, Y.Q.; data curation, S.L.; writing--original draft preparation, S.L.; writing--review and editing, W.Z. and Y.Q.; visualization, S.L.; supervision, Y.Q.; project administration, Y.Q.; funding acquisition, Y.Q. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by China NSFC projects under Grants 62122050 and 62071288, and in part by Shanghai Municipal Science and Technology Major Project under Grant 2021 SHZDZX0102 and in part by Jiangsu Technology Project (No.BE2022059-4).  
Not applicable.  
**Data Availability Statement:** No new data were created or analyzed in this study. Data sharing is not applicable to this article.