# Multiple Optimizations-Based ESRFBN Super-Resolution Network Algorithm for MR Images
## 1 Introduction  
MR images can detect small pathological tissue at an early stage, which is of great significance in the localization of pathological lesions and the diagnosis of disease. As MR images with high-resolution can provide clearer structural details, which can help doctors to analyze and diagnose the disease correctly, it is more desirable to obtain high-resolution MR images in a stronger magnetic field [1]. However, the acquisition of high-resolution MR images requires a stronger magnetic field and longer radiation scanning time. Generally, on the MR imaging time, it maybe lasts about 6-12 min for one organ region [2]. In this paper, the high-resolution refers to the resolution of an image for one organ region. For example, for the same size of the organ region, the low-resolution is 512 \(\times\) 512, and the high-resolution is 1024 \(\times\) 1024. When the imaging process takes a longer time, the movement of the human body during the process will bring more noise [3]. The improvement of the resolution of MR images will be at the cost of a doubling of the imaging time, which greatly reduces the patient's experience and easily bringspsychological pressure to the patient. When improving the resolution of MR images, the use of software to improve the resolution of MR images in this paper is a cost-effective method compared with the hardware method of upgrading the imaging equipment. Compared with traditional interpolation methods, such as Bicubic Interpolation and Nearest Neighbor Interpolation [4], as well as reconstruction-based methods, such as Convex Set Projection [5] and Maximum Posterior [6], the dictionary learning method has stronger feature expression, and can better characterize the mapping relationship between high- and low-resolution MR images [7]. Bicubic interpolation is the interpolation method in which the value of the function at the point (x, y) can be obtained by the weighted average of the 16 nearest sampling points in the rectangular grid. The nearest neighbor interpolation method is a gray value interpolation method, which makes the gray value of the transformed pixel equal to the gray value of the input pixel closest to it. Super-resolution reconstruction technology refers to the reconstruction of a corresponding high-resolution image from one or more low-resolution images based on reconstruction. This is mainly because the dictionary learning method can introduce the image's prior information from the trained data set, but its shallow model expression ability is limited; thus, the ability to learn the image's prior information is limited. In recent years, with the rapid development of deep learning technology, deep learning based super-resolution methods have been actively explored, which greatly promotes the development of image super-resolution technology. In 2014, [PERSON] et al. proposed the Super Resolution Convolutional Neural Network (SRCNN) model [8], which applied deep learning to the field of image super-resolution for the first time. Since then, scholars have carried out studies from the aspects of network architecture, loss function type, learning principle and strategy, etc. A large number of image super-resolution methods based on deep convolutional networks have been proposed, and they have been improving the performance of super-resolution continuously [9], such as Very Deep Super Resolution (VDSR [10]), Residual Dense Network (RDN) [11], Super Resolution Generative Adversarial Network (SRGAN) [12], Deep Back-projection Network (DBPN) [13] and Super Resolution Feed Back Network (SRFBN) [14], etc., which have reached the most advanced performance on various benchmarks of image super-resolution. In previous works, the researchers developed some MR super-resolution algorithms. We describe as follows. BIC [15]: The Bicubic Interpolation (BIC) method is to use the value of 16 pixels around the pixel to be calculated to estimate the value of the unknown pixel. It is a more complex interpolation method than the Nearest Neighbor Interpolation and Bilinear Interpolation.