# A Comprehensive Survey on Real-Time Image Super-Resolution for IoT and Delay-Sensitive Applications
## 2 Background  
### Overview of Super-Resolution  
SR is a method used to increase the resolution of digital photographs and videos in order to improve their quality [39]. This technique includes creating HR images from LR inputs, either from collected frames or in real-time [40]. It was developed from research conducted at AT&T Bell Laboratories in the 1990s. \"Super-resolution\" describes the technique of creating digital frames with HR to improve the spatial detail of the source image.  
In mathematical terms, if we denote an LR image as \(LR_{x}\), the degradation process can be modeled using a function \(D\). The corresponding HR image is represented as \(H_{x}\), and noise is accounted for by the variable \(\sigma\). This relationship can be expressed as Equation (1). To achieve HR outputs, various methods are employed, including reconstruction-basedmethods, interpolation-based methods, learning-based methods, example-based methods, and hybrid methods.  
\[LR_{x}=D(H_{x};\sigma) \tag{1}\]  
Several well-known methods are used to construct \(F\) outputs, including reconstruction-based, interpolation-based, learning-based, example-based, and hybrid-based methods. Figure 1 shows the taxonomy of the SR techniques and popular examples of each branch.  
Reconstruction-based SR methods are a subclass of SR that minimizes the difference between LR images and estimates the HR images [5]. This method uses an iterative approach that requires prior knowledge regarding the image in order to recover the HR frequencies that were lost during the process of LR image acquisition [41]. These methods utilize mathematical models that consist of a forward model and regulation term. In forwarding model, it describes the image formation process. This forward model consists of key factors such as the point spread of the system imaging, resolution of sensors, etc. On the other hand, a regulatory term is a mathematical function that is used in conjunction with a forward model to improve the smoothness of the HR picture. The optimization problem is defined by minimizing the dissimilarity between the LR images and the predicted HR image. This is subject to a regularization term. There are several well-known approaches introduced under reconstruction-based SR methods such as the Efficient Sub-Pixel Convolutional Neural Network (ESPCN) [42], Deep Recursive Residual Network (DRRN) [24], and Bayesian Image Super-Resolution (BSR) [43].  
The ESPCN architecture was introduced to upsample an LR image to an HR image by utilizing sub-pixel convolutional layers [42]. In this context, convolutional layers can learn to rearrange LR feature maps to generate HR images directly. This process reduces computational complexity. Apart from the ESPCN method, the DRRN is one of the popular methods that utilizes the Reconstruction-based SR method. In this approach, they constructed a recursive network that consists of several residual blocks. Every residual block consists of batch normalization and rectified linear unit (ReLU) activation layers. In 2001, the authors of [43] introduced the Bayesian framework for image SR, which can utilize prior distribution over HR images to regulate the solution. In this approach, they use a Laplacian distribution as the prior, which is characterized by a greater degree of smoothness in the HR image. In this case, the network applies the input image using a  
Figure 1: Taxonomy of the super-resolution techniques.  
two-step process to generate the HR output. As a first step, it upsamples the LR input by utilizing the linear interpolation method. The second stage uses a Bayesian framework to regulate the solution utilizing a prior distribution across HR photos.