# Generating Super Spatial Resolution Products from Sentinel-2 Satellite Images +
## 2 Materials and Methods
### Proposed Method  
In this section, we describe our experiments conducted to verify our methods. The method of generating the used dataset was explained in the past section. Generally, 6500 patches were collected and segregated into two sets, comprising 90% for training and 10% for testing for the purpose of validation. Therefore, for a better comparison, both the ESRGAN network and the proposed method were trained once. For a quantitative evaluation of the results, the well-known metrics of the Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) were used, which have been widely used in previous studies. Additionally, Spectral Angle Mapper (SAM) metrics were selected to assess the spectral quality.  
The ESRGAN [10] network was presented in 2018 by [PERSON] et al. The generator network architecture is in the post-upsampling framework. In the beginning, a convolutional layer is used as a feature extractor to generate 64 features with a kernel of 3 \(\times\) 3 dimensions and stride 1. Then, the generated features are input to a deeper feature extractor, which is composed of 23 Residual of Residual Dense Blocks (RRDBs). The RRDB blocks contain one residual architecture that uses three other residual architectures. Finally, after the upsampling layers, the extracted features are combined by two convolution layers, and the output of the network is obtained in the form of three features that represent three RGB spectral bands.  
Figure 1: Sample of LR-HR pairs from the dataset.  
In our proposed method, by extracting spatial features, such as the morphological profile and sharpening operation, we tried to reduce the pixelation in super-resolved images. Morphological analyses are designed using various shapes to extract information present in the form of spatial relationships between pixels. One common method in employing morphological analyses is to create a morphological profile. This means that different morphological operators are first applied to the image, and then their results are arranged alongside each other based on a specific pattern and utilized in a computational model [12]. In this study, we employed two morphological operators, Opening and Closing, to generate the morphological profile. For each of the three RGB spectral bands, these operators were applied three times, and their results were arranged sequentially, as shown in Figure 2.  
Additionally, we used the slope to prevent the degradation of land surface topography by the model. For this purpose, corresponding to each data, the Shuttle Radar Topography Mission (SRTM) v3 Digital Elevation Model (DEM) was acquired, and the regional slope was calculated. The use of the slope is advantageous compared to the elevation model because it has a threshold and can be applied without considering the image's position on the Earth.  
After preparing the required input data, fine-tuning and training the implemented model become crucial. In GAN networks, both the Generator (G) and Discriminator (D) networks are trained simultaneously. These networks engage in an adversarial relationship, striving to enhance each other's performance. Thus, maintaining equitable competition between them is of paramount importance. Therefore, initially, the G network was trained independently, and then the trained network was pitted against the D network.