# Image Magnification Based on Bicubic Approximation with Edge as Constraint
## 5 Experimental Results
### Numerical Accuracy (PSNR and SSIM)  
First, PSNR and SSIM are used as criteria to compare the magnified images. The 8 methods are used to magnify LR images twice, and the PSNR and SSIM values of the magnified images are calculated using HR images. The PSNR and SSIM values of the magnified images of 12 typical images are shown in Table 1, and the average PSNR and SSIM values of the images in BSD100, Urban100, and AIS are shown in Table 2, where the boldface indicates the maximum PSNR and SSIM values. The last row in Table 1 is the average of the PSNR and SSIM values for each method. When PSNR is used to measure image quality, the larger the PSNR value, the better the image quality, while when the image quality is measured in terms of SSIM, the larger the SSIM value, the higher the similarity \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Image**} & \multicolumn{2}{c}{**Bicubic**} & \multicolumn{2}{c}{**DCCI**} & \multicolumn{2}{c}{**ICBI**} & \multicolumn{2}{c}{**SelfExSR**} & \multicolumn{2}{c}{**NARM**} & \multicolumn{2}{c}{**SISRRFI**} & \multicolumn{2}{c}{**LPRGSS**} & \multicolumn{2}{c}{**New**} \\ \cline{2-13}  & **PSNR** & **SSIM** & **PSNR** & **SSIM** & **PSNR** & **SSIM** & **PSNR** & **SSIM** & **PSNR** & **SSIM** & **PSNR** & **SSIM** & **PSNR** & **SSIM** & **PSNR** & **SSIM** \\ \hline Baboon & 23.99 & 0.731 & 22.76 & 0.659 & 22.73 & 0.666 & 23.70 & 0.763 & 22.87 & 0.663 & 23.67 & 0.731 & 24.28 & 0.767 & **24.32** & **0.772** \\ \hline Barbara & 25.43 & 0.794 & 24.10 & 0.742 & 23.94 & 0.743 & 24.42 & 0.806 & 24.12 & 0.744 & 24.78 & 0.787 & **25.66** & **0.819** & 25.15 & 0.812 \\ \hline Boat & 32.28 & 0.917 & 29.42 & 0.879 & 29.42 & 0.882 & 32.66 & 0.928 & 29.52 & 0.879 & 32.95 & 0.903 & 32.72 & 0.926 & **33.13** & **0.930** \\ \hline Chest & 29.56 & 0.920 & 26.23 & 0.861 & 26.23 & 0.876 & 31.53 & 0.940 & 26.32 & 0.786 & 30.33 & 0.928 & 30.38 & 0.936 & **31.57** & **0.941** \\ \hline Couple & 29.66 & 0.860 & 27.50 & 0.807 & 27.47 & 0.810 & 29.94 & 0.872 & 27.61 & 0.805 & 28.82 & 0.843 & 30.04 & 0.876 & **30.33** & **0.880** \\ \hline Crowd & 32.82 & 0.945 & 28.64 & 0.896 & 28.77 & 0.902 & 34.03 & 0.957 & 28.74 & 0.894 & 32.39 & 0.928 & 33.51 & 0.954 & **34.35** & **0.960** \\ \hline Dollar & 20.42 & 0.670 & 19.41 & 0.623 & 19.30 & 0.622 & 20.31 & 0.694 & 19.51 & 0.629 & 20.61 & 0.675 & 20.62 & 0.698 & **20.69** & **0.701** \\ \hline Goldhill & 31.34 & 0.860 & 29.20 & 0.810 & 29.25 & 0.815 & 31.28 & 0.869 & 29.24 & 0.804 & 30.96 & 0.858 & 31.68 & 0.875 & **31.82** & **0.878** \\ \hline Kod & 26.51 & 0.861 & 24.73 & 0.822 & 24.49 & 0.822 & 26.90 & 0.881 & 24.88 & 0.826 & 26.86 & 0.855 & 26.91 & 0.879 & **27.22** & **0.884** \\ \hline Lake & 30.62 & 0.872 & 27.54 & 0.825 & 27.76 & 0.834 & 31.05 & 0.880 & 27.78 & 0.826 & 30.41 & 0.867 & 31.10 & 0.884 & **31.39** & **0.886** \\ \hline Lenna & 32.25 & 0.942 & 29.16 & 0.903 & 29.16 & 0.908 & 33.21 & 0.950 & 29.24 & 0.900 & 31.95 & 0.940 & 32.79 & 0.951 & **33.56** & **0.955** \\ \hline Peppers & 33.76 & 0.890 & 30.73 & 0.863 & 30.73 & 0.865 & 34.74 & 0.893 & 30.79 & 0.859 & 32.76 & 0.888 & 34.18 & 0.898 & **34.69** & **0.899** \\ \hline Average & 29.05 & 0.885 & 26.62 & 0.807 & 26.61 & 0.812 & 29.48 & 0.869 & 26.72 & 0.801 & 28.87 & 0.850 & 29.49 & 0.872 & **29.85** & **0.875** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM) values of 12 magnified images by 8 methods. Figure 3: Twelve typical images, from left to right, from top to bottom: Barbara, Baboon, Boat, Chest, Couple, Crowd, Dollar, Goldhill, Kod, Lake, Lenna, and Peppers. between the magnified image and the HR image. The results in Table 1 show that, in the 12 magnified images, except for Barbara, the PSNR and SSIM values of the new method are the largest and the average PSNR and SSIM value of the new method is also the largest.