## 3 Materials and Methods
### Denoising of Images  
The goal of denoising is to remove the noise from the image and recover the original image. This can be achieved by using a denoising model, which is trained to remove the noise added during the noise injection step. Image noise, which is usually electrical noise, is a random variation in the brightness or color information in photographs. It can be produced by the image sensor and circuitry of a scanner or digital camera [90]. Noise invariably reduces the quality of images, resulting in a decrease in visual image quality [91]. It should be noted that the impact of image noise manipulation on gaze distribution was mainly determined by noise intensity rather than noise type [92]. There are several types of noise models that can be used to add noise to images in deep learning, such as Gaussian noise, salt and pepper noise, and Poisson noise. Gaussian noise is the most used noise model, which is characterized by a normal distribution with a mean of zero and a standard deviation of \(\sigma\). It can be mathematically represented as follows:  
\[y=x+N(0,\sigma^{2}) \tag{1}\]  
where \(x\) is the original image and \(y\) is the noisy image. Salt and pepper noise is a type of noise that randomly sets certain pixels to the minimum or maximum value. The mathematical representation of salt and pepper noise can be represented as:  
\[y=x+Bernoulli(p)\times(rand-0.5) \tag{2}\]  
where \(x\) is the original image, \(y\) is the noisy image, \(p\) is the probability of noise, and \(rand\) is a random number between 0 and 1. Poisson noise is a type of noise that is typically added to images taken by sensors such as cameras. Poisson noise can be mathematically represented as:  
\[y=x+Poisson(\lambda x) \tag{3}\]  
Figure 5: Illustration of Cutmix and MixUp image augmentations. where \(x\) is the original image, \(y\) is the noisy image, and \(\lambda\) is the intensity of the noise. To test for model robustness, we added Gaussian noise from the Albumentations library to the training dataset to reduce the image features and see how well our model performs. Noise was added to the images during the training phase and this was usually performed by applying a noise model to each image in the training dataset. The noise model was usually applied to each pixel of the image, with the goal of simulating the noise that would be present in real-world scenarios. A loss function was used to measure the difference between the denoised image and the original image. The most commonly used loss function for image denoising is the mean squared error (MSE), which is defined as:  
\[MSE=\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2} \tag{4}\]  
where \(y\) is the original image, \(\hat{y}\) is the image denoised, and \(n\) is the number of pixels in the image. Finally, the denoising model was optimized by minimizing the loss function using gradient descent, a method for finding the minimum of a function by iteratively moving in the direction of steepest descent as defined by the negative of the gradient:  
\[\theta_{i}=\theta_{i-1}-\alpha\frac{\partial J(\theta)}{\partial\theta} \tag{5}\]  
where \(\theta\) is the parameter to optimize, \(J(\theta)\) is the loss function, \(\alpha\) is the learning rate, and \(\frac{\partial J(\theta)}{\partial\theta}\) is the loss function gradient with respect to the parameters. The negative of the gradient is used to find the steepest descent direction, and the learning rate \(\alpha\) determines the step size to take in that direction. The process is repeated until the function reaches a minimum. In general, the goal of adding noise to images in deep learning is to improve the robustness of the model by making it more resistant to the noise present in real-world scenarios. This is achieved by training the model on noisy images and by using denoising techniques to remove the noise during the testing phase.