## 4 Results
### Reconstruction Performance  
The dictionary \(\mathbf{D}\) and the programming configurations, including parameters such as the optimizer, minibatching, and maximum iterations, were kept consistent with the settings described in [32]. The RIRs were reconstructed up to a duration of 100 milliseconds. To provide a comprehensive performance comparison, nine different coupling structures, detailed in Table 1, were applied to reconstruct the sound fields. This evaluation offers a thorough analysis of the performance of these structures under various real-life environments. To assess reconstruction performance, two widely utilized metrics are employed. The first metric, the Normalized Mean Square Error (NMSE), quantifies the discrepancy between the reconstructed sound pressure \(\mathbf{p_{\bullet k}}\) and the reference sound pressure \(\widetilde{\mathbf{p}}_{\bullet k}\). It is mathematically represented as:  
\[\text{NMSE}=\frac{\|\mathbf{p_{\bullet k}}-\widetilde{\mathbf{p}}_{\bullet k} \|_{2}^{2}}{\|\widetilde{\mathbf{p}}_{\bullet k}\|_{2}^{2}}. \tag{26}\]  
The second metric, the Pearson Correlation Coefficient (PCC), evaluates the linear relationship between the reconstructed and reference sound pressures. The PCC is calculated using the following formula:  
\[\text{PCC}=\frac{\text{cov}(\mathbf{p_{\bullet k}},\widetilde{\mathbf{p}}_{ \bullet k})}{\sigma_{\bullet k}\widetilde{\sigma}_{\bullet k}}. \tag{27}\]  
where \(\text{cov}(\mathbf{p_{\bullet k}},\widetilde{\mathbf{p}}_{\bullet k})\) indicates the covariance, while \(\sigma_{\bullet k}\) and \(\widetilde{\sigma}_{\bullet k}\) represent the standard deviations of \(\mathbf{p_{\bullet k}}\) and \(\widetilde{\mathbf{p}}_{\bullet k}\), respectively. These metrics provide a comprehensive evaluation of the accuracy and consistency of the reconstruction results. The reconstruction performance of nine coupling structures is comprehensively evaluated across the DTU and UTS datasets using NMSE and PCC metrics, as presented in Tables 3 and 4 and Figures 1 and 2. CPC-ST consistently outperforms other structures, achieving the lowest NMSE and highest PCC values across both datasets and room configurations. This highlights its superior accuracy and robustness in reconstructing sound fields, especially in later stages where the sound field becomes more complex. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**DTU**} & **UTS** & **UTS** & **UTS** & **UTS** \\  & & **(Large Meeting** & **(Medium Meeting** & **(Small Meeting** & **(Shoebox Room)** \\  & & **Room)** & **Room)** & **Room)** \\ \hline Length & 7.50 m & 10.87 m & 7.36 m & 4.10 m & 11.75 m \\ Width & 4.74 m & 10.22 m & 5.61 m & 4.01 m & 6.00 m \\ Height & 2.80 m & 3.00 m & 3.00 m & 3.00 m & 3.00 m \\ \hline Reverberation Time & 0.4 s & 1.218 s & 0.659 s & 0.497 s & 0.667 s \\ \hline Original Sampling Rate & 44,100 Hz & 48,000 Hz & 48,000 Hz & 48,000 Hz & 48,000 Hz \\ \hline Resampling Rate & 8820 Hz & 8640 Hz & 8640 Hz & 8640 Hz & 8640 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Configurations for both datasets. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Coupling Structures**} & \multirow{2}{*}{**DTU**} & **UTS** & **UTS** & **UTS** & **UTS** \\  & & **(Large Meeting** & **(Medium Meeting** & **(Small Meeting** & **(Shoebox Room)** \\  & & **Room)** & **Room)** & **Room)** \\ \hline CPC-ST & 0.5355 & 0.6866 & 0.6691 & 0.6720 & 0.6657 \\ CPC-T & 0.5463 & 0.7202 & 0.6927 & 0.6896 & 0.6761 \\ CPC-S & 0.5407 & 0.6908 & 0.6773 & 0.6816 & 0.6699 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: NMSE of reconstruction methods across different coupling structures. For the DTU dataset, CPC-ST achieves an NMSE of 0.5355 and a PCC of 0.6830, outperforming other coupling structures like RPC-ST and APC-ST. In the UTS dataset, CPC-ST demonstrates a significant advantage in all room types, including the large, medium, and small meeting rooms, as well as the shoebox room.