## 4 Results and Discussion of the Nasal Cavity Three-Dimensional Structure Reconstruction System
### Results and Analysis of Nasal Acoustic Signal Preprocessing
The reconstruction results for the straight tube model and the simulated nasal cavity model are shown in Figures 13 and 14, respectively. From Figures 13 and 14, it can be seen that the existence of the DC offset component causes the error in the cross-sectional area to increase as the depth of the nasal cavity increases. The reason for this is that the nasal cavity three-dimensional structure hierarchical reconstruction method is an iterative method that needs to be solved by using the parameters related to the previous depth layer to solve for the current depth layer. If there is an obvious error in the initial value or at a specific point, the error in the final iteration will progressively increase. Moreover, when the value of the constraint factor \(q\) is too small, high-frequency noise is also involved in the iterative operation, resulting in poor smoothness of the two-dimensional depth-cross-sectional area curve in the reconstruction. Conversely, when the value of the constraint factor \(q\) is too large, the input impulse response sequence curve is under-fitted, which leads to the two-dimensional depth-cross-sectional area curve being too smooth and the amplitude significantly deviating from that of the standard curves. For instance, the simulated nasal cavity model exhibits sharp bends at both the minimum and maximum cross-sectional area points. These sharp bends result in rapid transitions in the cross-sectional area, making it more susceptible to high-frequency noise and the DC offset component. When the constraint factor \(q\) is excessively large, it suppresses too  
Figure 12: (**a**) Partial input impulse response frequency spectrum of the straight tube model. (**b**) Partial input impulse response time sequence of the straight tube model. (**c**) Partial input impulse response frequency spectrum of the simulated nasal cavity model. (**d**) Partial input impulse response time sequence of the simulated nasal cavity model. much high-frequency information, resulting in a two-dimensional depth-cross-sectional area curve that is too flat at the bends, failing to reflect the changes at the sharp bends. The error statistics of the reconstructed result and the actual physical model under different preprocessing methods are shown in Tables 1 and 2. Figure 14: Reconstruction results of two-dimensional depth–cross-sectional area curves of the simulated nasal cavity model. Figure 13: Reconstruction results of two-dimensional depth–cross-sectional area curves of the straight tube model. From Table 1, it can be seen that the depth-cross-sectional area root mean squared error and mean relative error of the reconstructed result are significantly reduced by eliminating the DC offset component and introducing a moderate value of constraint factor when compared with the actual physical size of the straight tube model. The root mean squared error decreases to 0.0201 cm\({}^{2}\), while the mean relative error reduces to 1.8248%. Compared to the results without any preprocessing method, there is a 96.8014% reduction in root mean squared error and a 45.8219% decrease in mean relative error. Furthermore, the maximum relative error and minimum relative error are significantly reduced. The results show that the depth-cross-sectional error distribution of the reconstructed result is very uniform, and the algorithm has strong stability in the effective measurement depth. From Table 2, it can be seen that all the depth-cross-sectional area error indicators of the reconstructed result are significantly reduced by eliminating the DC offset component and introducing a moderate value of constraint factor when compared with the actual physical size of the simulated nasal cavity model. The root mean squared error decreases to 0.1510 cm\({}^{2}\), while the mean relative error reduces to 3.3096%. Compared to the results without any preprocessing method, there is a 96.8364% reduction in root mean squared error and a 104.5086% decrease in mean relative error.