## 3 Results and Discussions  
In addition to visual interpretation, various image quality metrics were used for the test images improved by the trained model in SR studies, although based on statistical analysis results that are not positively supported by visual interpretation become inadequate especially in solving real-world problems [44], meaning that the image with a higher quality metric is not always visually better [15]. The most commonly used image quality metrics in SR studies are the Root Mean Squared Error (RMSE) [45], Peak Signal-to-Noise Ratio (PSNR) [46], and Structural Similarity Measure Index (SSIM) [47]. The RMSE value is a metric used to measure the similarity or difference of pixel values between two images. RMSE with a positive value and a smaller  
Figure 5: SRCNN design. value indicates that two images are closer or similar to each other [44,48]. RMSE is the square root of MSE, and is calculated accordingly:  
\[\text{RMSE}=\sqrt{\left(\frac{1}{n}\right)\times\sum(Y_{i}-X_{i})^{2}} \tag{1}\]  
where:  
\(Y_{i}\) represents the value of the data point in HR;  
\(X_{i}\) represents the value of the data point in the test image;  
n represents the total number of data points. PSNR measures the representativeness of the image. The higher the PSNR value, the higher the similarity between two images and the better the quality is considered. However, PSNR has a disadvantage in that it does not reflect the quality perceived by the human eye [48,49]. It is usually expressed in dB (decibels), and is calculated by the formula below:  
\[\text{PSNR}=10\times\text{log}10((\text{M2})/\text{MSE}) \tag{2}\]  
where:  
M represents the maximum possible value of pixel values;  
MSE (Mean Squared Error) represents the mean square error between the HR and the test image. SSIM attempts to measure the structural similarity between two images, and expresses this similarity as a score. It takes a value in the range [0, 1], where 1 indicates the highest similarity and best quality while 0 indicates the lowest similarity and worst quality. Its calculation includes three components: luminance similarity, contrast similarity, and structural similarity. Luminance similarity measures the similarity between the luminance components of two images, and includes differences in pixel values and contrast. Contrast similarity measures the similarity between the contrast components of two images, and refers to the standard deviation of pixel values. Structural similarity measures the similarity of two images, and involves the correlation and similarity of pixel values. By combining these three components, SSIM produces an overall similarity score [47,48]. The higher the SSIM score between two images, the higher the similarity and quality. Universal Image Quality Index (UIQI) [49] is another metric used to evaluate image quality. This metric determines the quality of an image using brightness and contrast distortion as well as correlation loss. Unlike pixel-based metrics, it can produce negative values. Although it adopts a similar approach to SSIM, UIQI focuses mainly on color-based features, while SSIM considers more details and fine features [47,48]. The fifth metric used in the study is the Bhattacharyya distance value [50], which is a statistical metric that measures the similarity or difference between two probability distributions. It is used to evaluate overlap or separate distributions. Values range from 0 to \(\infty\), with a smaller Bhattacharyya distance indicating that two distributions are more similar and a larger distance indicating more dissimilarity or separation. Both images are represented in a color space. They are separated into color components and a histogram is calculated for each color component. The histograms show the distribution of the pixel values of each color component, and are normalized by scaling each histogram to a sum of 1.