## 3 Results
### Synthesized Data Experiments
#### 3.2.1 Quantitative Comparisons Using Synthesized S2 Data  
The data for this experiment, seen in Figure 6g, were simulated using an AVIRIS image with 5 m resolution employing methods similar to [5, 6]. The original AVIRIS image of an area near San Diego, CA, was acquired in November 2011. It is 790 \(\times\) 6796 pixels with 5 m resolution in 224 bands that span a spectral range of 366-2496 nm that covers the range of the S2 sensors. The S2 version was simulated by applying the S2 spectral response to a patch of the AVIRIS data depicting parts of the city of Escondido and its suburbs. Twelve bands of size 648 \(\times\) 648 pixels at a spatial resolution of 5 m were obtained. These bands were filtered and subsampled and cropped to yield 252 \(\times\) 252 pixel ground truth for all bands at 10 m resolution. The bands were then filtered using a 12 \(\times\) 12 Gaussian approximation of the S2 sensor PSF from [49], and downgraded to yield four bands of size 252 \(\times\) 252 pixels at 10 m resolution, six bands of size 126 \(\times\) 126 pixels at 20 m resolution, and two bands of size 42 \(\times\) 42 pixels at 60 m resolution. Because the PSF blur is applied to the synthesized image in a near identical manner to that modeled by the ATPRK, SupReME, S2 Sharp, MuSA, and SSSS methods, those methods should be expected to perform particularly well on this data. The tuned version of S2 SSC also uses the same PSF blur during training. Sen2 res and DSen2, on the other hand, do not explicitly model the S2 PSF in the same way, so they could be expected to perform worse. Table 3 shows a comparison between the super-resolution methods. SupReME gets the best results for the 60 m bands while ATPRK does slightly better for the 20 m bands. Based on average RMSE for all bands, the methods ordered by performance are S2 Sharp, ATPRK, SupReME, SSSS, MuSA, DSen2, and Sen2 res. For the 20 m bands ATPRK is followed by S2 SSC, slightly outperforming S2 Sharp. Otherwise, the order remains mostly the same apart from MuSA and SSSS trading places. For 60 m band performance, SupReME is followed by S2 Sharp, SSSS, ATPRK, MuSA, Sen2 res, and DSen2. Figure 6: RGB images of the synthetic datsets used, generated from bands B2, B3 and B4 using a combination of methods described in [52, 53]. SSSS shows particularly strong results in the 60 m bands, getting the best UIQI, SSIM, and SRE scores for B1. DSen2, in contrast, does very badly in band B1 and has the lowest average 60 m SRE of all the methods, while Sen2 res does slightly worse in all other metrics. ATPRK, MuSA, S2 Sharp, S2 SSC, SSSS, and SupReME all get very high 20 m UIQI and SSIM scores, with only bands B11 and B12 presenting a significant challenge. Depending on the application, any of these methods might be useful for the lower wavelength 20 m bands but based on the low RMSE and high SRE values, ATPRK, S2 SSC, and S2 Sharp have a clear advantage. As noted, due to the lack of PSF modeling, Sen2 res and DSen2 were expected to perform slightly worse than the competing methods. For all data, running times are dominated by DSen2. It processes this particular data in approximately half a second. The slowest method by far is MuSA, which takes almost  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & **ATPRK** & **DSen2** & **MuSA** & **S2 Sharp** & **S2 SSC** & **SSSS** & **SupReME** & **Sen2 res** \\ \hline RMSE\(\downarrow\) & 20 m & **40.18** & 85.38 & 59.95 & 44.67 & 41.20 & 69.91 & 53.04 & 116.95 \\  & 60 m & 50.33 & 113.28 & 99.11 &  
25 min to process the same image. The other methods are much quicker, taking about 15 s each, apart from SSSS which takes slightly under 1 min. Error maps showing a graphical representation of the error between the estimates of each method and the reference ground truth as logarithmically scaled residual images, calculated using \(\mathbf{e}=\log\left(1+255\frac{\hat{\mathbf{\gamma}}-\mathbf{\gamma}}{1000}\right)\), can be seen in Figures 7 and 8. These residual images for bands B9 and B12, respectively, are shown on a scale of 0 to 4.