## 5 Conclusions  
This paper proposed an MTU-Net-based single-channel SE method that extended the conventional U-Net by employing a framework of multi-task learning. The proposed MTU-Net provided estimates of clean speech and noise magnitude spectra. Thus, the estimated clean speech was directly reconstructed using the estimated clean speech magnitude spectrum. In addition, an IRM or IBM was estimated by the ratio between the estimated clean spectrum and the sum of the estimated clean and noise spectra, thus allowing the clean speech to be estimated by applying the IRM or IBM to the noisy input spectrum. The performance of the proposed MTU-based SE method was evaluated under matched and mismatched noise conditions and compared to the performance of other neural network-based SE methods, such as DRNN-, SEGAN-, and conventional U-Net-based SE. Consequently, it was shown that the PESQ and STOI scores of the proposed SE method were higher than those of the other SE methods under both matched and mismatched conditions. Under matched noise conditions, the MTU-based SE method with IRM increased the average PESQ by 0.17, 0.52, and 0.40 compared to DRNN, SEGAN, and U-Net, respectively. Moreover, the average STOI score of the proposed SE method was higher by 0.07, 0.05, 0.05 compared to DRNN, SEGAN, and U-Net, respectively. Next, the IRM estimated by the proposed MTU-Net-based SE method was utilized for VAD. In other words, the proposed VAD method operated in an unsupervised manner by using the by-product of the proposed SE method. To compare the performance of the proposed VAD with that of the supervised learning-based methods using deep neural networks such as DNN, bDNN, and LSTM, each was trained using noisy speech utterances under the matched noise condition. Here, the proposed SE method was applied to noisy speech utterances as a front-end for the deep neural network-based VAD methods. The comparison showed that the proposed VAD method offers similar detection performance (measured by the AUC and ERR) for whatever noise contaminates the noisy speech utterances, while the performance of the deep neural network-based VAD methods degrades significantly under the mismatched noise condition. To improve the performance of the proposed MTU-Net-based SE method, especially under mismatched noise conditions, future studies should employ an online noise adaptation technique using non-negative matrix factorization [39]. Conversely, the domain adversarial training technique [40] should be incorporated into the proposed SE method. In future work, to further improve the performance of the proposed MTU-Net-based SE method, the MTU-Net should incorporate a type of online noise adaptation using non-negative matrix factorization [39] or domain adversarial training [40]. In addition, the effect of the proposed \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**AUC (\%)** & **\(\mathbf{-5}\) dB** & **0 dB** & **5 dB** & **10 dB** & **Average** \\ \hline Noisy + DNN & 81.05 & 86.02 & 88.94 & 91.43 & 86.86 \\ Noisy + bDNN & 79.05 & 85.10 & 87.85 & 90.59 & 85.65 \\ Noisy + LSTM & 80.60 & 86.37 & 89.02 & 90.84 & 86.71 \\ MTU-Net + DNN & 79.52 & 84.79 & 87.24 & 89.22 & 85.19 \\ MTU-Net + bDNN & 79.42 & 84.63 & 87.11 & 89.11 & 84.69 \\ MTU-Net + LSTM & 79.45 & 85.18 & 87.20 & 89.16 & 85.25 \\ Proposed mask-based VAD & 84.60 & 88.04 & 89.88 & 89.13 & 87.91 \\ \hline
**EER (\%)** & **\(\mathbf{-5}\) dB** & **0 dB** & **5 dB** & **10 dB** & **Average** \\ \hline Noisy + DNN & 27.56 & 23.21 & 19.82 & 16.32 & 21.73 \\ Noisy + bDNN & 30.30 & 24.41 & 21.98 & 19.75 & 24.11 \\ Noisy + LSTM & 27.39 & 22.20 & 19.92 & 18.05 & 21.89 \\ MTU-Net + DNN & 29.40 & 25.32 & 23.82 & 21.84 & 25.10 \\ MTU-Net + bDNN & 30.77 & 25.95 & 23.94 & 22.44 & 25.78 \\ MTU-Net + LSTM & 30.50 & 25.51 & 24.20 & 22.83 & 25.83 \\ Proposed mask-based VAD & 22.74 & 19.36 & 18.16 & 18.71 & 19.74 \\ \hline \hline \end{tabular}
\end{table}