# Multi-View Synthesis of Sparse Projection of Absorption Spectra Based on Joint GRU and U-Net
## 4 Results and Discussion  
### Image Reconstruction Results  
The projection data with different specifications in the test set were fed into the trained GMResUNet model to generate the multi-angle projection data matrix (N = 32). As shown in Figures 10-12, the synthesized typical single-peak, double-peak, and multi-peak temperature field multi-angle projection data and error map distributions under the conditions of N = 2, 4, 8, and 16 are shown, respectively, with the generated multi-angle projection data on the left and the corresponding relative error distributions on the right. Table 1 shows the average relative errors of the four sparse projection data for the three temperature field modes. relative error were also used as specific metrics to evaluate their quality for temperature field reconstruction. Figure 10: Synthesis results and error distributions of four sparse projections of the single-peak temperature field. (**a**) N = 2; (**b**) N = 4; (**c**) N = 8; (**d**) N = 16. Figure 11: Synthesis results and error distributions of four sparse projections of the bimodal temperature field. (**a**) N = 2; (**b**) N = 4; (**c**) N = 8; (**d**) N = 16. Figure 12: Synthesis results and error distributions of four sparse projections of the multi-peak temperature field. (**a**) N = 2; (**b**) N = 4; (**c**) N = 8; (**d**) N = 16. The U-Net was used to evaluate the effect of the synthesized temperature field reconstruction, as shown in Figures 14-16, which represent typical single-peak, double-peak, and multi-peak temperature fields reconstructed under the N = 2, 4, 8, and 16 conditions, as well as the relative error plots. The network input projection data correspond to the multi-angle projection data synthesized in Figures 10-12. Table 2 shows the reconstruction errors of the three temperature fields. The results show that the reconstruction error of the temperature field was less than 2% for N = 4 and above, and the reconstruction error of the single-peak and double-peak temperature fields was less than 3.5% for the extremely sparse projection probe with N = 2. This means that this sparse projection synthesis method can be widely applied to synthesize probe data for various distributions. The basic trend of the reconstruction error was to increase with the increase in the complexity of the temperature field and to decrease with the increase in the number of projections, N. However, the reconstruction error of the multi-peak complex temperature field under the condition of N = 2 was still less than 7%, although the synthesis of its corresponding projection data was less effective. On the other hand, the error of the highest temperature peaks with drastic changes was slightly larger than that of the places with gentle changes, which may be determined by the theory of molecular absorption spectroscopy, where the absorption sensitivity of molecules decreases with an increasing temperature. Especially in the case of the extremely high temperature of 2600 K in the present simulation, the neural network may not be able to decouple the feature mapping of higher-temperature values very well [36; 37]. \begin{table}
\begin{tabular}{c c c c} \hline
**Projection Angle N** & **Single-Peak Distribution** & **Bimodal Distribution** & **Multimodal Distribution** \\ \hline N = 2 & 3.12\% & 2.43\% & 6.50\% \\ N = 4 & 2.77\% & 2.08\% & 1.98\% \\ N = 8 & 1.13\% & 1.16\% & 1.54\% \\ N = 16 & 0.73\% & 1.12\% & 1.13\% \\ \hline \end{tabular}
\end{table} 
Table 2: Distribution error of temperature field reconstruction after synthesis of four sparse projections for three temperature field modes. Figure 13: U-Net temperature field reconstruction model for test projection data. \begin{table}
\begin{tabular}{c c c c} \hline
**Projection Angle N** & **Single-Peak Distribution** & **Bimodal Distribution** & **Multimodal Distribution** \\ \hline N = 2 & 0.79\% & 0.77\% & 1.81\% \\ N = 4 & 0.24\% & 0.37\% & 0.41\% \\ N = 8 & 0.13\% & 0.20\% & 0.23\% \\ N = 16 & 0.16\% & 0.18\% & 0.19\% \\ \hline \end{tabular}
\end{table}