# Multi-View Synthesis of Sparse Projection of Absorption Spectra Based on Joint GRU and U-Net
## 4 Results and Discussion
### Evaluation of Indicators  
In order to quantitatively analyze the effects of multi-angle projection data synthesis, the _PSNR_, _SSIM_, and error of the -angle data synthesis metrics for different sparse projections were calculated on the test set with 2000 samples. As shown in Table 3, we applied three methods to calculate the _PSNR_, _SSIM_, and error of different sparse projections for N = 2, 4, 8, and 16 data, respectively, and the results are the average values of 2000 data on the test set. The three synthesized methods are the interpolation method, the UNet, and the GMResUNet.  
In Table 3, it can be seen that the results of the interpolation method were the worst in all three metrics, while the UNet performed better than the interpolation method, and GMResUNet performed the best among the three. Regarding errors, the GMResUNet had the lowest results, the interpolation method had significantly higher results, and the UNet performed well. These results show that the GMResUNet can maintain high-quality synthesis of sparse to multi-angle projections and achieve further improvement of the projection data.  
In order to evaluate the quality of temperature field reconstruction of the synthesized multi projection data, the synthesized multi-angle projection data were also subjected to temperature field reconstruction on the test set with a sample of 2000. As shown in Table 4, we applied two methods to calculate the evaluation metrics of the temperature field under N = 2, 4, 8, and 16, and the results are the average values of the test set. Two of the synthesized methods were based on traditional CNN and U-Net and were specially trained for temperature field reconstruction in this paper. It can be observed that as the sparse angle N increased, the results of both the CNN and the U-Net reconstruction became significantly better, with the _PSNR_, _SSIM_, gradually increasing, and the error gradually decreasing. This proves that our proposed GMResUNet can realize the improvement of sparse projection, and thus, maintain the high quality of temperature field reconstruction in the sparse TDLAS technique for tomographic imaging tasks.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Projection** & **Methods** & **PSNR** & **SSIM** & **Error** \\
**Angle N** & & & & \\ \hline \multirow{2}{*}{N = 2} & CNN & 28.510 & 0.921 & 5.00\% \\  & U-Net & 30.503 & 0.942 & 3.74\% \\ \hline \multirow{2}{*}{N = 4} & CNN & 31.543 & 0.954 & 3.45\% \\  & U-Net & 34.969 & 0.964 & 2.07\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Quality analysis of reconstructed images with different algorithms.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Projection** & **Methods** & **PSNR** & **SSIM** & **Error** \\
**Angle N** & & & & \\ \hline \multirow{2}{*}{N = 2} & Interpolation & 20.139 & 0.446 & 18.26\% \\  & UNet & 30.823 & 0.814 & 2.16\% \\  & GMResUNet & 32.996 & 0.985 & 0.96\% \\ \hline \multirow{2}{*}{N = 4} & Interpolation & 25.694 & 0.592 & 13.62\% \\  & UNet & 34.456 & 0.835 & 1.31\% \\  & GMResUNet & 40.726 & 0.997 & 0.35\% \\ \hline \multirow{2}{*}{N = 8} & Interpolation & 28.536 & 0.603 & 8.03\% \\  & UNet & 38.144 & 0.867 & 0.54\% \\  & GMResUNet & 44.977 & 0.998 & 0.20\% \\ \hline \multirow{2}{*}{N = 16} & Interpolation & 32.585 & 0.780 & 5.34\% \\  & UNet & 43.684 & 0.933 & 0.32\% \\ \cline{1-1}  & GMResUNet & 46.572 & 0.998 & 0.18\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Effects of multi-angle projection data synthesized by different methods.