# Integrating Dilated Convolution into DenseLSTM for Audio Source Separation
## 4 Experiments
### Speech Experiment
#### 4.1.4 Experimental Results of the Objective Measures for Speech Enhancement  
In speech recognition after speech enhancement, objective indicators (PESQ, SDR, STOI, NCM, SCII, and WER) were measured for GRN, MMDenseLSTM, DiDenseNet, proposed architecture, and MMDenseLSTM+, which increased only the number of parameters in MMDenseLSTM. Table 4 shows the number of parameters for each architecture. The proposed architecture had 50% more parameters than MMDenseLSTM because it is an architecture in which dilated blocks are added to MMDenseLSTM. Since the performance may be improved simply by increasing the parameters of MMDenseLSTM, we designed MMDenseLSTM+ having almost the same number of parameters as the proposed architecture to confirm this. MMDenseLSTM+ has the same architecture as MMDenseLSTM, and the hyper-parameter (growth rate, compression rate, the number of composite function) was properly adjusted. \begin{table}
\begin{tabular}{c c c c c} \hline
**Model Comparison** & **Hard** & **Medium** & **Easy** & **Total** \\ \hline Proposed \textgreater{} DiDenseNet & 0.60 (\(**\)) & 0.60 (\(*\)) & 0.59 (\(*\)) & 0.60 (\(***\)) \\ \hline Proposed \textgreater{} MMDenseLSTM & 0.61 (\(**\)) & 0.67 (\(***\)) & 0.62 (\(**\)) & 0.63 (\(***\)) \\ \hline Proposed \textgreater{} GRN & 0.89 (\(***\)) & 0.79 (\(***\)) & 0.71 (\(***\)) & 0.80 (\(***\)) \\ \hline DiDenseNet \textgreater{} MMDenseLSTM & 0.57 (n.s.) & 0.51 (n.s.) & 0.42 (n.s.) & 0.50 (n.s.) \\ \hline DiDenseNet \textgreater{} GRN & 0.79 (\(***\)) & 0.79 (\(***\)) & 0.68 (\(***\)) & 0.76 (\(***\)) \\ \hline MMDenseLSTM \textgreater{} GRN & 0.88 (\(***\)) & 0.82 (\(***\)) & 0.88 (\(***\)) & 0.86 (\(***\)) \\ \hline \end{tabular}
\end{table} 
Table 3: Result of subjective listening test. “Hard” indicates an environment that music and noise are mixed at 0 dB, “Medium” mixed at 5 dB, and “Easy” mixed at 10 dB (”n.s.”: not significant, “\(*\)”: \(p<0.05\), “\(**\)”: \(p<0.01\), “\(***\)”: \(p<0.001\)). Figure 5 compares the results of PESQ, SDR, STOI, NCM, SCII, and WER for each deep learning architecture and an unprocessed mixture signal in 0 dB SMR and SNR environments. MMDenseLSTM+ showed the best performance among the deep learning architectures in SDR results and showed the same or better performance than MMDenseLSTM in PESQ, STOI, and CSII, but showed lower NCM, WER performance than MMDenseLSTM, DillDenseNet, and the proposed architecture. Therefore, we can see that simply increasing the parameter did not improve the performance. In addition, GRN had more than twice the parameters of the proposed architecture but showed the lowest performance among deep learning architectures. Lastly, the proposed architecture showed lower performance than MMDenseLSTM and MMDenseLSTM+ in SDR, but it had the best performance in other results. In particular, the proposed architecture in WER showed a relatively 14.4% improvement in performance compared to MMDenseLSTM, and it showed the best performance compared to other deep learning architectures. Overall, PESQ, STOI, CSII, and NCM performance showed a higher correlation with WER results than SDR performance, and especially NCM had the highest correlation. The matched pairs sentence-segment word error test [58] using the NIST speech recognition scoring toolkit (SCTK) ([[https://github.com/usnistgov/SCTK](https://github.com/usnistgov/SCTK)]([https://github.com/usnistgov/SCTK](https://github.com/usnistgov/SCTK))) was performed to confirm the statistical significance in the WER results of Figure 5. In the comparison between the proposed architecture and DillDenseNet, the \(p\)-value was less than 0.01, and in the comparison between the proposed architecture and other deep learning architectures, the \(p\)-value was less than 0.001 in all cases. Therefore, in the WER results of Figure 5, the difference in performance between the proposed architecture and other deep learning architectures was statistically significant.