## 1 Introduction  
Super-resolution (SR) is the process of improving a low resolution (LR) image to a high resolution (HR) image without altering the originality of the image. This super-resolution is also called hallucination [1]. The process of converting a low-resolution image to a high-resolution image is necessary during image processing [2], and it has a wide range of applications. In satellite image processing, image restoration and image enhancement require super-resolution to remove distortions and for enhancement of satellite images [3]. Super-resolution has wide applications in medical image processing for improving the quality of medical images, such as MRI CT scan, which requires more contrast and fine enhancements [4]. Its multimedia applications are also increasing, wherein all multimedia, e.g., images, videos, and animation require high definition when the SR functionality is involved [5]. Face hallucination must have the following constraints:  
1. Data constraints: The output image of face hallucination must be similar to the input after completion of smoothening and downsampling. 2. Global constraint: It must have the same features of the human face, e.g., mouth, nose, and eyes. The face features must be steady. 3. Local constraint: The final image must have the exact characteristics of a face image with the local feature. Video surveillance cameras are used widely in many places, such as banks, stores, and parking lots, where intensive security is critical [6]. Details of facial features obtained from the surveillance video are essential in identifying personal identity [7]. However, in many cases, the images obtained from the surveillance cameras cannot be well identified due to the low resolution of facial images that cause the loss of facial features [8]. Thus, to obtain detailed facial features for personal recognition, it is necessary to infer a low-resolution (LR) facial image to a high-resolution (HR) using by face hallucination or face super-resolution [9]. Such techniques are applied in a variety of essential sectors, e.g., medical imaging, satellite imaging, surveillance system, image enlarging in web pages, and restoration of old historic photographs [10]. Due to limited information on image identification, reconstruction and expression analysis is a challenge to both humans and computers. Under some circumstances, it is impossible to obtain image sequences [11]. Several super-resolution reconstruction (SRR) researches have been proposed, relying on two approaches: reconstruction-based and learning-based approach [12]. The reconstruction-based approach employs multiple LR images of the same object as an input for reconstructing an HR image. In contrast, the learning-based approach uses several training samples from the same domain with different objects to reconstruct the HR image [13]. An advantage of the learning-based approach is its ability to reconstruct the HR image from the single LR image. Learning-based super-resolution is applied to human facial images [14]. Several related facial hallucination methods have been proposed in recent years. Learning-based methods have acquired more considerable attention as they can achieve high magnification factors and produce positive super-resolved results compared to other methods [15]. The related facial hallucination methods may be used on position-patches to improve image quality [16]. Such methods perform a one-step facial hallucination based on the position-patch instead of neighbor-patch. A patch position is one of the learning-based approaches that utilize the facial image, as well as image features, to synthesize high-resolution facial images from low-resolution ones [17]. In comparison, neighbor patches are used widely in face hallucination. The reconstruction of a high-resolution facial image could be based on a set of high and low-resolution training image pairs [18]. The high-resolution image is generated using the same position image patches of each training image [19]. This method can be extended using bilateral patches [20].