## 4 Proposed Methodology
### Pre-Processing
#### 4.1.1 Enhanced Super-Resolution Generative Adversarial Network (ESRGAN)  
Pre-processing is a crucial step for the enhancement of images which helps in achieving superior performance metrics [26]. The Super-Resolution Generative Adversarial Network (SRGAN) is a foundational technique which can generate photorealistic patterns while super-resolving a single picture. The reckoning of a high resolved image from a low-resolution image is termed a super-resolution. The major optimization focus of super-resolution is to cut back the mean square error from the obtained highly resolved image and original image. GANs offer a potent framework for creating realistic pictures that seem believable and have excellent perceptual quality [27]. The visual hallucinated features, though, are very often associated with undesirable effects [28]. The Enhanced SRGAN is the adaptive technique which mainly addresses the three shortcomings of SRGAN that are Adversarial loss, Network design, and Perceptual loss. It also facilitates maintenance of a better ocular peculiarity with more pragmatic and natural-looking colors than SRGAN. To achieve the Enhanced Super-Resolution Generative Adversarial Network (ESRGAN), [PERSON] et al. introduced an additional Residual layer in Residual Dense Block (RDB) in [28] by removing the Batch Normalization (BN) layer. The Residual in Residual Dense Network (RRDN) comprises four different blocks, namely Dense Feature Fusion, Residual Dense Blocks, Shallow Feature Extraction, and up-sampling net [29]. The Local Feature Fusion layer and the Local Residual Learning layer are the two dense layers that form the RRDB. Local Feature Fusion (LFF): It is an adaptive state derived from RRDB and a convolution layer in a new RRDB and is given by Equation (1). \[f_{d,LF}=h^{D}_{LFF}\big{(}\{f_{d-1},\ f_{d,1},\ldots\ldots,\ f_{d,c},\ldots.,f_{d,C}\}\big{)} \tag{1}\]  
where \(h^{D}_{LFF}\) indicates the convolution layer of size \(1\times 1\) in the dth RRDB block and \(f_{d-1}\), \(f_{d,1}\), etc., are the input and output of dth RRDB correspondingly. Local Residual Learning (LRL): It is implemented for the improvement of overall information flow. It also helps to get the final output of dth RRDB as shown in Equation (2). \[f_{d}=\big{(}\{f_{d-1}+f_{d,LF}\}\big{)} \tag{2}\]  
Other than the improvement of visual qualities using RRDB, [PERSON] et al. also calculated different loss functions which gave the overall performance of the generator. The different loss functions are stated as [29]. 1. Discriminator loss: It is the loss calculated during misclassification of real and fake instances. Some of the fake instances are obtained from the generator by expanding the equation given in Equation (3). \[l_{D}^{Ra}=-E_{x_{r}}\Big{(}log\Big{\{}D_{Ra}\Big{\{}x_{r},x_{f}\Big{\}}\Big{\}} \Big{)}-E_{x_{f}}\Big{(}log\Big{\{}1-D_{Ra}\Big{\{}x_{f},x_{r}\Big{\}}\Big{\}} \Big{)}\] (3) where \(log\Big{\{}D_{Ra}\Big{\{}x_{r},x_{f}\Big{\}}\Big{\}}\) is the probability of classification by generator correctly and \(log\Big{\{}1-D_{Ra}\Big{\{}x_{f},x_{r}\Big{\}}\Big{\}}\) helps to accurately label the fake images from the generator. 2. Generator loss: The generator loss is calculated if the discriminator misclassifies the fake images which helps the discriminator to improvise. It is given by Equation (4) \[l_{G}^{Ra}=-E_{x_{r}}\Big{(}log\Big{\{}1-D_{Ra}\Big{\{}x_{r},x_{f}\Big{\}}\Big{\}} \Big{)}-E_{x_{f}}\Big{(}log\Big{\{}D_{Ra}\Big{\{}x_{f},x_{r}\Big{\}}\Big{\}} \Big{)}\] (4) It is observed that the generator can achieve better results from both real and generated data in adversarial training. 3. Perpetual Loss: In ESRGAN, the perpetual loss is also improved by confining the features prior to activation, as compared to features after activation in SRGAN. The perpetual loss function is given by Equation (5). \[l_{G}=l_{percep}+\lambda l_{G}^{Ra}+\eta l_{1}\] (5) where the terms \(\lambda\) and \(\eta\) are the factors to equalize various loss functions and \(l_{G}^{Ra}\) is the generator loss function. 4.