## 3 Results
### Synthesized Data Experiments
#### 3.2.2 Evaluating Effects of Parameter Tuning  
The parameter tuning method was evaluated for each of the super-resolution methods by testing them on the 7 datasets seen in Figure 6. The 6 additional synthesized S2 datasets were originally used for testing some of the methods in their original papers and their generation is described in greater detail in Appendix A. These images all come with ground truths and were super-resolved using both default and tuned parameters.  
Parameter tuning was performed as previously described and the boxplots of Figure 9 show a comparison of the SRE values for each method. While ATPRK, MuSA and SupReME show almost no improvements, S2 Sharp, S2 SSC, and SSSS show significant gains from the use of parameter tuning method.  
ATPRK performs a parameter search of its own to select the best values for the semivariograms used to generate the kriging matrix. The parameters being tuned here merely provides initialization for that search which might explain why ATPRK does not show much of an improvement. Parameter tuning does not appreciably improve MuSA performance and tweaking the single \(\lambda\) parameter of SupReME does not seem to affect the  
Figure 8: Absolute error map of Escondido crop, band B12, on log scale. Lower values are better.  
Figure 9: Boxplot showing the distribution of SRE in dB for all the synthetic datasets for each of the methods. Higher values are better. S2 SSC is only evaluted for 20 m bands but other methods include values for both 20 and 60 m bands.  
results in any significant manner either. These methods may also have already been tuned to the ideally suited parameters.  
Focusing on the mean SRE, represented by a line inside each box on the boxplot, S2 Sharp, S2 SSC, and SSSS all benefit greatly from the use of tuned parameters. Unlike the related MuSA method the selection of different \(\lambda\) and \(\mu\) is very effective for SSSS. The end results still remain rather unimpressive compared to the other methods, even with tuning. SSSS appears ill suited for the type of synthetic data being tested.  
For a fixed number of iterations, the tuning being performed on the S2 SSC batch size and learning rate is probably affecting how quickly the network finds a solution more than the quality of the solution. The improvement is mainly a result of the change in how training images are generated. Using PSF modeling for the synthesized data increases the methods performance significantly. It should still be reiterated that S2 SSC only processes the 20 m bands.  
S2 Sharp goes from middling, using default parameters, to leading performance when tuned. The performance boost is to be expected as the method was developed with an associated parameter tuning method presented in [5] and not really intended to be used with the default parameters for all data. As was shown in [28] the parameter tuning method used here can further improve its results.  
Broadly, Figure 9 shows that with tuning S2 Sharp gives the best results, on average, and S2 SSC does best for the 20 m bands. Without tuning ATPRK, MuSA, and SupReME can potentially perform better. The other methods, DSen2, Sen2 res, and SSSS do not perform as well.