## 3 Results and Discussion  
Figure 2 shows the ultrasound images obtained by applying the algorithms to improve the spatial resolution of the ultrasound phantom image acquired using the Field 2 program. The phantom image consisted of a point target, cyst region, and strongly reflecting region. To demonstrate the spatial resolution improvement efficiency of the proposed MSDEPC algorithm, the bicubic interpolation method [41] and SRCNN [21] were compared. Bicubic interpolation is a traditional interpolation method that applies the product of the intensity value of an adjacent pixel and its weight according to distance. Sixteen adjacent intensity values are required to determine the value of one pixel. The existing interpolation method can be used effectively by applying appropriate boundary conditions and constraints to the interpolation kernel. The SRCNN uses three convolution layers and a ReLU [42] activation function. The kernel size of each convolution layer was 9 \(\times\) 9, 1 \(\times\) 1, and 5 \(\times\) 5, with a stride of 16 and an initial learning rate of 0.003; in addition, the Adam optimizer was implemented in this study. Table 1 shows the computation times of the bicubic interpolation method, SRCNN, and the MSDEPC algorithm. When GPUs were used, the MSDEPC algorithm was approximately 0.72 times slower than SRCNN, and the CPU was about approximately  
0.8 times slower. This is due to an increase in the model parameters, which did not affect the result. In the case of the bicubic interpolation method, there was no significance in the comparative measurements at very high computational speeds. By visually analyzing the acquired images, we confirmed that the spatial resolution improved when using the algorithms compared to the LR images. In particular, we confirmed that blurring was significantly reduced in most areas of the phantom image when the proposed MSDEPC algorithm was used. To quantitatively analyze the degree of spatial resolution improvement of the MSEDPC algorithm, the intensity profile was obtained and the FWHM was calculated. Figure 3 shows the intensity profile and FWHM results measured from the simulated ultrasound phantom images obtained using the various spatial resolution improvement algorithms. The line profile is represented graphically using \"line AB\" in Figure 2. As shown in Figure 3a, the profiles of the SRCNN and MSDEPC algorithms are sharper than those of the images obtained using LR and bicubic interpolation. In addition, the proposed MSDEPC algorithm showed a slightly sharper profile in the edge areas than the SRCNN. The graph in which the sigma value was derived from the profile obtained is shown in Figure 3a, and the graph from which the FWHM values were calculated is shown in Figure 3b. The FWHM values that accurately represented the spatial resolution were calculated as 0.800, 0.781, 0.472, and 0.452 using the LR, bicubic, SRCNN, and proposed MSDEPC algorithms, respectively. Similar to the visual evaluation results, the best FWHM value was derived from the ultrasound simulation phantom image using the MSDEPC algorithm, which was approximately 1.77 times better than the one obtained from the LR image. Figure 4 shows the PSNR and SSIM graphs calculated from the resulting ultrasound images based on Field 2 simulation. The PSNR values obtained using the simulated images were 7.73, 11.93, 17.50, and 26.32 for the LR, bicubic, SRCNN, and proposed MSDEPC algorithms, respectively. Following the same trend as the FWHM data, the best PSNR value was obtained using the MSDEPC algorithm, and an improvement of approximately 3.40 times compared to LR was confirmed. The SSIM values obtained using the simulated image were calculated to be 0.652, 0.776, 0.840, and 0.906 for the LR, bicubic, SRCNN, and proposed MSDEPC algorithms, respectively. Owing to the characteristics of the SSIM method, which indicate superior similarity as the value approaches 1, the