# Hyperspectral Image Super-Resolution Based on Spatial Group Sparsity Regularization Unmixing
## 5 Results and Analysis
### Hyperspectral Unmixing
We give the mean and standard deviation for each quality metric in Table 3. The best results are shown in bold. Note that Table 3 gives an evaluation of the overall image quality, while Figure 9 shows a visual comparison in a single band. Hence, it is reasonable that the subjective evaluation of Figure 9 might be inconsistent with some of the metrics in Table 3. This inconsistency does not affect the conclusions of the quantitative quality evaluation. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Methods** & **FUSE** & **BSR** & **CSU** & **CMS** & **LTR** & **Ours** \\ \hline \multirow{2}{*}{SSIM} & 0.99902 & 0.99943 & 0.99989 & 0.99995 & 0.99991 & **0.99996** \\  & \(\pm\) 7.74 \(\times\) 10\({}^{-4}\) & \(\pm\)6.9\(\times\)10\({}^{-4}\) & \(\pm\)1.84\(\times\) 10\({}^{-4}\) & \(\pm\)1.13\(\times\)10\({}^{-4}\) & \(\pm\)1.23\(\times\)10\({}^{-4}\) & \(\pm\)**3.61\(\times\)10\({}^{-5}\)** \\ \hline \multirow{2}{*}{RMSE} & 0.48136 & 0.28558 & 0.23279 & 0.22475 & 0.24432 & **0.21031** \\  & \(\pm\)0.13070 & \(\pm\)0.078466 & \(\pm\)0.07063 & \(\pm\)0.06109 & \(\pm\)0.06109 & \(\pm\)**0.02689** \\ \hline \multirow{2}{*}{PSNR} & 29.56316 & 38.62009 & 41.01761 & 41.81752 & 40.41452 & **42.74880** \\  & \(\pm\)4.23725 & \(\pm\)5.45638 & \(\pm\)5.27647 & \(\pm\)5.81294 & \(\pm\)5.52129 & \(\pm\)**2.89850** \\ \hline \multirow{2}{*}{SAM} & 2.95474 & 4.21175 & 2.62583 & 2.44085 & 2.69322 & **2.25826** \\  & \(\pm\)0.793651 & \(\pm\)1.31910 & \(\pm\)0.86600 & \(\pm\)0.75043 & \(\pm\)0.76777 & \(\pm\)**0.58335** \\ \hline \multirow{2}{*}{ERGAS} & 2.78576 & 1.38858 & 1.08028 & 0.91274 & 1.02112 & **0.86787** \\  & \(\pm\)1.21321 & \(\pm\)0.69591 & \(\pm\)0.71299 & \(\pm\)0.47246 & \(\pm\)0.49095 & \(\pm\)**0.52625** \\ \hline \multirow{2}{*}{Q2\({}^{n}\)} & 0.53836 & 0.75601 & 0.81238 & 0.80453 & 0.78496 & **0.82477** \\  & \(\pm\)0.10412 & \(\pm\)0.09046 & \(\pm\)0.06793 & \(\pm\)0.06697 & \(\pm\)0.07007 & \(\pm\)**0.05305** \\ \hline Time (s) & 10.66 & 8157.12 & 1358.69 & 1388.09 & 1631.74 & 2369.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average quantitative results of the compared methods on the Harvard data set. Figure 8: Super-resolution results for impe1 in the Harvard data set. It can be seen, from the numerical results in Table 3, that the proposed method had superior performance to the compared methods, in terms of all quality metrics. All of the methods performed well in terms of SSIM. The superiority in SSIM values demonstrates that the spatial structures of the estimated hyperspectral images were well-recovered by the proposed method. Our method achieved a significantly lower average RMSE than all other compared methods. It reduced the error by about 6.4%, compared to the best baseline and improved at least 56.3% against all others. The superiority in RMSE indicates that our estimated image had the closest pixel values to the ground truth in all spectral bands. The average PSNR of the proposed method was 0.93-11.01 db (2.22% to 37.25%) larger than that of the other methods. This indicates that the super-resolution results obtained by the proposed method were closer to the ground truth, in terms of spatial numerical similarity. SSIM, RMSE, and PSNR all mainly evaluate performance in terms of spatial information. This improvement is a result of using the SLIC superpixel algorithm in our method. Spatially adjacent pixels are clustered, in order to take advantage of preserving structures or features with similar structures. SAM evaluates the quality of spectral reconstruction. It can be seen that the average SAM value of the proposed method was lower than that of the compared methods. Our average SAM value was reduced by 46.38% to 7.48%, compared to the other baselines. The superiority in spectral similarity of the proposed method comes from the sparsity priors by coupling a spatial group sparsity regularizer with sparse unmixing. ERGAS and \(Q2^{n}\) are global quality metrics, which not only evaluate the spatial structure but also the spectral similarity.