## 1 Introduction
Sentinel-2 Parallel Residual Network [16] (SPRNet) trains two sets of parallel residual networks with lower scale data synthesized from the S2 data, obtaining good spatial fidelity and spectral preservation. The paper [17] was inspired by DSen2 and develops two large neural networks for deployment and training on high performance computing clusters, one for 20 m bands and one for 60 m bands. Furthermore, inspired by DSen2, ref. [18] suggests a single convolutional neural network for super-resolving the 20 and 60 m Sentinel-2 bands to 10 m simultaneously. Figure 1: Sentinel-2 spectral response characteristics from [1] alongside earth surface solar irradiance from [3]. Spatial resolution and central spectral wavelength of each band appear in parentheses in the legend. Variants of Generative Adversarial Networks [19] (GAN) have also been suggested for S2 sharpening. A deep convolutional design for a GAN that gives good results for the super-resolution of S2 images was developed in [20]. Sentinel-2 Generative Adversarial Network [21] (S2 GAN) similarly uses the 10 m S2 bands as guidance for learning the super-resolution task on lower resolution bands. A GAN method inspired by [22] that focuses solely on the S2 10 m RGB bands was developed in [23]. It is trained using PeruSat-1 images with 2.8 m resolution as a reference to resolve S2 images. When comparing different methods, finding the best parameters for each method can be a daunting task, particularly if a method has many parameters or if the user is not intimately familiar with all the nuances of the method. We present a framework that allows for fair comparisons between different methods by attempting to ensure optimal performance is achieved by each method. Having a framework that can be applied across different methods of super-resolution, or even different capture platforms makes an objective comparison of methods easier. In this paper, we propose a tuning parameter selection method using [PERSON]'s protocol [24] by first reducing the scale of the image being processed 2\(\times\) and 6\(\times\). Bayesian optimization [25] with a Tree-structured Parzen Estimator [26; 27] (TPE) is used to find the parameters that give the best results when resolving the 20 and 60 m bands back to their original resolution and applied to super-resolving the original full scale image. A preliminary version of this parameter selection approach was described in [28]. Our code is available on the first author's github page ([[https://github.com/[PERSON]/s2-sr-parameter-optimization](https://github.com/[PERSON]/s2-sr-parameter-optimization)]([https://github.com/[PERSON]/s2-sr-parameter-optimization](https://github.com/[PERSON]/s2-sr-parameter-optimization)), accessed on 3 June 2021). The proposed parameter selection approach is used to select tuning parameters for six S2 sharpening methods, i.e., SupReME, S2 Sharp, MuSA, SSSS, ATPRK and S2 SSC. These methods along with Dsen2, and Sen2 res are critically compared using standard comparison criteria. The code used to generate these comparisons will be made available for download. Adding new methods through simple wrapper functions is easy and allows for both parameter optimization and direct comparisons between methods. While the focus in this paper is on Sentinel-2 images these same principles could also be applied to other types of multispectral multiresolution satellite data, e.g., MODIS, ASTER, Landsat-7, and Landsat-8 [29; 30; 31]. The paper is organized as follows. Section 2 describes the tuning parameter selection approach and the comparison methods. Section 3 compares the qualities of the methods and describes the quantitative metrics used to compare them. Quantitative comparisons use synthesized and reduced scale S2 data. For qualitative comparisons, real S2 images are used. This is followed by the final conclusions in Section 4.