## 1 Introduction  
Ultrasound refers to frequencies above 20,000 Hz, which is higher than the human hearing range and is widely used in diagnostic medicine. Ultrasound imaging used in the diagnostic medical field is referred to as ultrasonography, and organs of the human body are observed in the frequency range of 2-18 MHz [1]. Although the use of ultrasound imaging to observe the human body was established later than the use of radiography, it has recently been in the spotlight as an imaging technique that allows for the relatively easy observation of lesions through a nondestructive and noninvasive examination method. Since diagnostic ultrasound imaging technology was first used in obstetrics and gynecology,it has been used in all medical fields, including those pertaining to the abdomen, breast, thyroid, and blood vessels [2; 3; 4; 5; 6]. Various methods are available for acquiring diagnostic ultrasound images [1]. Among these, the brightness mode (B-mode) expresses the intensity of the reflected wave as a two-dimensional brightness image. B-mode ultrasound images are used to diagnose lesions, and efforts are needed to improve image quality and diagnostic accuracy. Spatial resolution is an important evaluation index for ultrasound image quality, and methods to improve it include thickening the damping layer of the pulse-wave probe or using systems that improve the basic frequency [7]. In addition, ultrasound images can be acquired using multiple focal points to improve lateral resolution, or additional acoustic lenses can be installed to improve the slice thickness resolution [8]. However, when the damping on the ultrasonic probe is increased, the bandwidth of the sound beam widens and the quality factor decreases, and increasing the frequency shortens the penetration depth. In addition, when the focal length of the sound beam is increased, the disadvantage of lowering the temporal resolution inevitably decreases. Recently, software and technologies have been widely used to overcome the shortcomings of hardware-based spatial-resolution improvement methods. Super resolution (SR) is one of the primary methods [9]. This technique overcomes the inherent resolution limitation of low-resolution (LR) imaging systems. The main advantage of this approach is that it is inexpensive and can be simply utilized with existing LR imaging systems. The SR image reconstruction problem expresses the degradation model between LR and high-resolution (HR) images as follows [9; 10; 11]:  
\[y=Wx+n,\ W=DBM, \tag{1}\]  
where \(y\) denotes the LR image generated from the HR image \(x\), with resolution degradation factor \(W\), and additional noise \(n\). The matrices comprising \(W\) are \(D\) for the subsampling matrix, \(B\) for the blur matrix, and \(M\) for the warp matrices. SR is the process of predicting the optimal \(W\) and \(n\), and the most basic method is multi-image-based SR [12]. Interpolating multiframe images to an HR image grid to improve resolution has the advantage of enabling SR based on real-world information. However, it is difficult to generate an HR image using this approach because it does not always match the even HR grid, and noise can interfere with matching [13]. However, example-based SR does not require this process. This is a learning-based approach to image enlargement in which the training set consists of pairs of LR and HR images. Generally, a detailed HR image is acquired and downsampled to account for the degradation of \(W\) and \(n\), as shown in Equation (1). The size is matched to the HR image using an existing interpolation method (e.g., linear or bilinear) to design a training dataset [14]. High-frequency information, which is mainly related to resolution, is distorted between LR and HR images, and several methods have been introduced, including Bayesian, prior-based, dictionary learning, and self-similarity methods [15; 16; 17; 18].