## 2 Related Work and Contributions
### Super-Resolution  
Several SISR methods have been proposed to recover an HR image from a single LR image. These methods can be broadly divided into handcrafted methods and deep learning methods. Early handcrafted SISR methods include interpolation-based methods, statistics-based methods, and example-based methods. Interpolation-based methods, such as bilinear [12], bi-cubic [13], and edge-directed interpolation [14], estimate HR by interpolating LR pixels to HR pixels. These types of methods tend to generate overly smooth or blurry image. Statistics-based methods (e.g., [15]) learns the statistical relationship of the gradient profile between the HR and LR images, motivated by the idea that shape statistics of the gradient profiles is invariant to the image resolution. These types of images tend to produce watercolor-like artifacts when applied to visually complex images. Finally, example-based methods use conventional machine-learning algorithms, such as Random Forests (RFs) [16; 17; 18] and Markov Random Fields (MRFs) [19], to learn the mapping from LR to HR images. These methods tend to generate a reconstructed image that contains irrelevant (hallucinated) details. Recently, convolutional neural networks (CNNs) and generative adversarial networks (GANs) have been used to learn the mapping from LR to HR images. For example, [PERSON] et al. [20] proposed the first SR-CNN network to efficiently learn this mapping. [PERSON] et al. [21] proposed a CNN model, known as very deep super-resolution (VDSR), to predict the mapping from LR to HR images using residual learning. Inspired by the VGG architecture [22], VDSR has 20 layers and is trained using extremely high learning rates. VDSR achieved state-of-the-art performance and outperformed SR-CNN [20]. It also resolved several issues of SR-CNN [20] such as the utilization of contextual information from a small image region, slow convergence, and the need for training individual scale-dependent models. A GAN-based network, named P-SRGAN, has been proposed [23] recently to learn the mapping from LR to HR images. P-SRGAN consists of a generator network and a discriminator network. The generator network takes an LR image as input and generates the HR image while the discriminator compares the generated image with the HR image to generate good quality reconstructed images. Although this approach achieved excellent performance, GAN-based networks are hard to train due to the Nash equilibria problem. This problem is defined as a zero-sum game between the generator network (player 1) and the discriminator network (player 2) where the opponent players contest with each other in a game to improve their objective functions [24]. In addition, GAN-based networks are highly sensitive to the hyperparameter selection and often get into mode collapse (i.e., the generator maps different inputs to the same output) [24]. To regularize the training of GAN-based SR models and enforce the right mapping between the input and output domains, [PERSON] et al. [25] proposed GAN-CIRCLE network for constructing HR CT images from their LR counterparts. The proposed network combines four loss functions, viz., adversarial loss, cycle-consistency loss, identity loss, and joint sparsifying transform loss, to stabilize training and enforce the right input-output mapping. Expert radiologists evaluation of GAN-CIRCLE on three CT datasets demonstrates its ability in constructing HR images from noisy LR input images. Although the usage of GAN-CIRCLE solved regular GANs training and mapping problems, this network is computationally complex and requires a relatively large GPU as well as much longer training time in comparison to the regular-GAN networks. Further, the network failed to faithfully recover subtle structures in CT images as discussed in [25]. We refer the reader to [26; 27] for comprehensive reviews of other handcrafted and deep learning SISR methods.