## 3 Results
### Real Data Experiments
#### 3.1.2 Quantitative Comparisons Using Reduced Scale S2 Data  
To make a quantitative comparison of semi-real S2 data, two reduced scale versions of the same S2 image were generated. First a 1620 \(\times\) 2124 crop from the data was chosen and reduced resolution versions of all bands were generated at both 2\(\times\) pixel size and 6\(\times\) pixel size. This was done by applying appropriate filters to simulate the PSF of each S2 band to their appropriate bands before downgrading by a factor of 2 and 6, respectively.  
The blurring being applied is nearly identical to that modelled in the ATPRK, SupReME, S2 Sharp, MuSA, and SSSS methods. These data are also scaled to the same scales as the data used for the training process of the DSen2 neural network, while S2 SSC will downgrade the data even further for training. If scale invariance holds, this should not affect the results greatly, but the model based methods and DSen2 may still have a slight advantage. A further crop to 216 \(\times\) 216 pixels for \(\Upsilon^{\text{D}}_{10m}\), 108 \(\times\) 108 in \(\Upsilon^{\text{D}}_{20m}\), and 36 \(\times\) 36 in \(\Upsilon^{\text{D}}_{60m}\) was then made for each version of the image, mainly to shorten the running times.  
The results can be seen in Tables 1 and 2, the best results on each line are bold. Although the reduction methods used are the same as for the synthetic data in the following subsection, the errors are much larger for semi-real data. One obvious difference is that here all bands are processed to even lower resolution scales. The scale reduction of the 10 m bands may also be adversely affecting the upscaling processes. The characteristics of real S2 data appear to be worse represented at reduced scales than by synthesized data like that used in the following subsection.  
Based on average RMSE for the 40 \(\rightarrow\) 20 m task, the methods ordered by performance are S2 SSC, S2 Sharp, ATPRK, SupReME, MuSA, DSen2, Sen2 res, and SSSS, as seen in Table 1. SSSS performs significantly worse than its relatives, S2 Sharp, SupReME, and MuSA. All methods give fairly good UIQI and SSIM results. For both metrics, the best performances are in bands B6, B7 and B8A. The wavelengths captured in bands B7 and B8A are a subset of the wavelengths captured by the 10 m band B8, as can be seen in Figure 1, and B6 is spectrally close. For SRE, the metric being optimized during parameter tuning, ATPRK, S2 SSC, and S2 Sharp outperform all other methods by some margin in every 20 m band. None of the methods manage to get an ERGAS below 3 for this task, which would be considered a good score.  
Table 2 shows that the results are quite different for the 360 \(\rightarrow\) 60 m task. MuSA and SSSS perform comparatively well, SSSS giving the best results, followed by MuSA, DSen2, SupReME, S2 Sharp, ATPRK, and Sen2 res. ATPRK does not perform as well for this data at a greatly reduced scale as for other data tested and in fact the magnitude of the RMSE is greatly increased at this scale for all methods apart from SSSS. ERGAS scores are also fairly high (lower is better) and SRE scores are low (higher is better) for all methods. UIQI and SSIM are also much worse than with the smaller scale reduction, particularly for DSen2 and Sen2 res.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & & **ATPRK** & **DSen2** & **MuSA** & **S2 Sharp** & **S2 SSC** & **SSSS** & **SupReME** & **Sen2 res** \\ \hline RMSE\(\downarrow\) & 20 m & 144.02 & 206.95 & 194.04 & 140.60 & **132.80** & 210.79 & 165.46 & 253.24 \\ SAM\(\downarrow\) & 20 m & 4.48 & **4.17** & 5.56 & 4.48 & 4.19 & 6.36 & 4.72 & 4.38 \\ ERGAS\(\downarrow\) & 20 m & 5.79 & 8.14 & 7.98 & 5.53 & **5.23** & 8.43 & 6.51 & 9.81 \\ Time \(\downarrow\) & Average & 11.39 & **0.45** & 1095.93 & 10.49 & 13.58 & 39.90 & 4.13 & 11.74 \\  & STD & 0.25 & 0.00 & 16.52 & 0.28 & 0.62 & 0.44 & 0.03 & 0.33 \\ \hline \end{tabular}
\end{table}
Table 1: Evaluation using reduced scale S2 data: Reduced by 2, super-resolved 40 \(\rightarrow\) 20 m. The best results are given in bold typeface.