# LSTNet: A Reference-Based Learning Spectral Transformer Network for Spectral Super-Resolution
## 4 Experiments and Results
### Comparison Experiment of Simulation Data  
We evaluated the performance of the proposed method with several baseline SSR methods on the simulation and real data. To investigate the performance fully, one traditional method and four CNN-based methods were used for comparison: Arad [19], AWAN [46], HRNet [47], FMNSSR [26], MSSR [27], and StiNet [24]. The parameters for all of the methods were tuned to their optimal values. **Pavia University data. ** First, the visual quality of the compared results was obtained for the Pavia University data. Figure 7 shows the reconstruction results under different indicators. The first row of Figure 7 shows the RGB images of different reconstruction results. It was found that, except for HRNet, the algorithms did not show any particular difference in the reconstruction of RGB images. Therefore, the error colormap was used to depict the reconstruction effect of different methods. The second and third rows represent the MRAE and SAM errors of the reconstruction results, respectively. The last three rows show the MSE errors in the different bands of the reconstructed image. The results demonstrate that HRNet and StiNet produced serious object boundary errors. Material-dependent errors were present in the results of MSSR and FMNSSR. In comparison, the results of Arad, AWAN, and the proposed method had fewer errors. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Component Modules** & \multicolumn{3}{c}{**Accuracy Indicators**} \\ \hline
**STM** & **Hard Attention** & **Soft Attention** & **mPSNR** & **SAM** \\ \hline ✓ & ✗ & ✗ & 40.6894 & 3.6826 \\ ✓ & ✓ & ✗ & 41.2751 & 3.4154 \\ ✓ & ✗ & ✓ & 41.4929 & 3.2163 \\ ✓ & ✓ & ✓ & **42.8197**1  & **2.1273**1  \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Ablation study on the Pavia University data set. Table 2 summarizes the quality assessment comparison obtained when using the Pavia University data. The mPSNR indicator represents the reconstruction quality of spatial information, while the SAM indicates the spectral reconstruction quality. A similar trend to that observed in the visual comparison can be seen in the quality assessment comparison. HRNet and StiNet had the worst reconstruction quality, while MSSR and FMNSSR had a similar reconstruction quality. Arad, AWAN, and the proposed method showed stable, high-quality reconstruction results. **University of Houston data**. The visual quality comparison for the University of Houston data is shown in Figure 8. Compared with the Pavia University data, the reconstruction result obtained using MSSR suffered the worst performance. This indicated that the performance of MSSR was affected by the sensors and the ground object materials. In contrast, the results of HRNet and FMNSSR showed better performances for these data. Compared with the Pavia University data, StiNet has a better reconstruction result on these data. The visual result of Arad presented the edge error for the ground object. AWAN and the proposed method yielded the best visualization reconstruction results. In contrast, the single-band comparison in the last three rows indicates that the proposed method achieved slightly better visualization results. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Arad** & **MSSR** & **FMNSSR** & **StiNet** & **HRNet** & **AWAN** & **Proposed** \\ \hline mPSNR & 41.3532 & 36.0617 & 36.1042 & 31.3055 & 29.1888 & 42.2823 & **42.8197**1 \\ SAM & 3.1857 & 4.2996 & 3.9235 & 5.3270 & 6.1036 & 2.3701 & **2.1273**1 \\ ERGAS & 8.1241 & 11.5657 & 11.4860 & 19.0757 & 23.3450 & 6.5043 & **6.3161**1 \\ RMSE & 0.0121 & 0.0163 & 0.0161 & 0.277 & 0.0354 & **0.0088**1 & **0.0088**1 \\ \hline \hline \end{tabular}  
* The best results are shown in bold.  
\end{table} 
Table 2: Quality assessment comparison on the Pavia University data set. Figure 7: Visual comparison of the results for different methods on the Pavia University data set. As presented in Table 3, the quantitative results were similar to those of the visual quality comparison.