## 4 Results and Discussion of the Nasal Cavity Three-Dimensional Structure Reconstruction System
### Results and Analysis of Nasal Acoustic Signal Preprocessing
The results show that both the elimination of the DC offset component and a moderate value of constraint factor \(q\) can significantly improve the accuracy of the nasal cavity three-dimensional structure hierarchical reconstruction method. However, the above results still contain errors, possibly due to the presence of low-frequency noise, which is difficult to eliminate. The results of the reconstruction were analyzed in detail using the simulated nasal cavity model, which is more consistent with the actual nasal cavity structure than the straight tube model. Figure 15 shows the relative error of the hierarchical reconstruction results of the simulated nasal cavity model at key measurement points under different preprocessing methods. By eliminating the DC offset component and introducing a moderate value of constraint factor, the method not only extends the effective measurement depth but also improves the reconstruction accuracy of the depth-cross-sectional area. As shown in Figure 15, when the DC offset component is not eliminated or the constraint factor is not introduced, the method is unable to reconstruct the cross-sectional area at a depth of 13 cm because the \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Preprocessing Methods**} \\ \cline{2-4}
**Errors** & **Uncorrected DC Offset** & **Elimination of DC Offset** & **Elimination of DC Offset** \\  & **No Constraint Factors** & **No Constraint Factors** & **Moderate Value of** \\  & **Introduced** & **Introduced** & **Constraint Factor** \\ \hline Root mean squared error (cm\({}^{2}\)) & 0.6284 & 0.1545 & 0.0201 \\ Maximum relative error (\%) & 91.8108 & 48.1741 & 4.1950 \\ Minimum relative error (\%) & 17.9650 & 0.2356 & 0.0441 \\ Mean relative error (\%) & 47.6467 & 9.0237 & 1.8248 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Errors in reconstructed results with the straight tube model under different preprocessing methods. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Preprocessing Methods**} \\ \cline{2-4}
**Errors** & **Uncorrected DC Offset** & **Elimination of DC Offset** & **Elimination of DC Offset** \\  & **No Constraint Factors** & **No Constraint Factors** & **Moderate Value of** \\  & **Introduced** & **Introduced** & **Constraint Factor** \\ \hline Root mean squared error (cm\({}^{2}\)) & 4.7730 & 3.5619 & 0.1510 \\ Maximum relative error (\%) & 681.9042 & 121.7401 & 8.7100 \\ Minimum relative error (\%) & 27.6178 & 0.3094 & 0.0163 \\ Mean relative error (\%) & 107.8128 & 69.2997 & 3.3096 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Errors in reconstructed results with the simulated nasal cavity model under different preprocessing methods. increased high-frequency noise is not suppressed. With the elimination of the DC offset component and the introduction of a moderate value of the constraint factor, the effective measurement depth of the nasal cavity reconstruction method is extended to 13 cm, and the correction effect is obvious at the starting point (0 cm), half-way point (7 cm), and the endpoint (13 cm). Compared to the uncorrected DC offset component and not introducing the constraint factor method, the accuracy of the cross-sectional area reconstruction at the starting point is improved by 43%, the relative error at the half-way point is reduced to 1.7% and the accuracy is improved by 178.3%, and the endpoint still maintains a low relative error of 1.9%. In consideration of the nasal cavity three-dimensional structure hierarchical reconstruction method is an iterative method. In this experiment, errors caused by the DC offset component and high-frequency noise will both gradually accumulate. This eventually leads to a significant error in the reconstruction results. When the value of the introduced constraint factor is moderate, the cumulative error caused by high-frequency noise will be significantly reduced, thus improving the reconstruction accuracy at deeper distances.