# Multiple Optimizations-Based ESRFBN Super-Resolution Network Algorithm for MR Images
## 3 Experimental Results and Analysis  
### Experiment 1  
In this section, the loss function experiments of L1, L2, SSIM, MS-SSIM and L1+MS-SSIM are performed on the double cubic down-sampling data set and K-space truncated data set. The specific experimental results are shown in Tables 1-4. When ESRFBN uses cascading loss function L1+MS-SSIM as a loss function for training, the effect is optimal on both the bicubic decrement sampling data set and K-space truncated data set, which indicates the effectiveness of the optimization of the cascading loss function. SSIM, as a loss function, is not particularly sensitive to uniform deviations, which will cause changes in brightness or color, and usually become duller. However, SSIM can preserve contrast and is better than other loss functions in the high-frequency region. On the other hand, the L1 loss function can keep the brightness and color unchanged. Therefore, the cascaded loss function can combine the characteristics of the two well, so that the super-resolution effect of the trained network is better. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Data** & **Scale** & **Bicubic** & **L1** & **L2** & **SSIM** & **MS-SSIM** & **L1+MS-SSIM** \\ \hline \multirow{2}{*}{neck} & \(\times\)2 & 25.44 & 37.89 & 40.41 & 40.24 & 40.15 & **40.47** \\  & \(\times\)4 & 21.58 & 30.28 & 30.90 & 30.50 & 30.67 & **30.92** \\ \hline \multirow{2}{*}{breast} & \(\times\)2 & 28.56 & 35.13 & 41.46 & 42.90 & 42.83 & **42.97** \\  & \(\times\)4 & 20.50 & 30.78 & 32.88 & 32.60 & 32.91 & **32.93** \\ \hline \multirow{2}{*}{knee} & \(\times\)2 & 30.60 & 38.39 & 40.12 & 40.04 & 40.12 & **40.20** \\  & \(\times\)4 & 22.69 & 31.42 & 32.63 & 32.29 & 32.51 & **32.64** \\ \hline \multirow{2}{*}{head} & \(\times\)2 & 20.32 & **39.42** & 38.55 & 38.19 & 38.28 & 39.39 \\  & \(\times\)4 & 18.60 & 34.04 & 32.97 & 32.20 & 31.95 & **34.11** \\ \hline \hline \end{tabular} Note: The numbers in bold are the best results.  
\end{table} 
Table 1: PSNR values of different loss functions (bicubic downsampling). As can be seen from Figure 3, compared with SSIM and MS-SSIM loss functions, the result of L1 and L2 only improves the pixels around the contour details, while for the result of SSIM and MS-SSIM loss functions, the feature details of high-resolution images after super-resolution are more prominent than that of L1 and L2. However, the L1+MS-SSIM loss function retains both pixel gray level information and contour feature information, and the image after super-resolution is most similar to the original image. It also indicates that the ESRFBN super-resolution network based on the L1+MS-SSIM cascading loss function optimization can effectively improve the super-resolution effect of MR images. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Data** & **Scale** & **Bicubic** & **L1** & **L2** & **SSIM** & **MS-SSIM** & **L1+MS-SSIM** \\ \hline \multirow{2}{*}{neck} & \(\times\)2 & 0.6500 & 0.8923 & 0.8979 & 0.8997 & 0.8980 & **0.8998** \\  & \(\times\)4 & 0.3399 & 0.8201 & 0.8255 & 0.8292 & 0.8268 & **0.8315** \\ \hline \multirow{2}{*}{breast} & \(\times\)2 & 0.4967 & 0.9123 & 0.9211 & 0.9206 & 0.9189 & **0.9213** \\  & \(\times\)4 & 0.0487 & 0.8027 & 0.8078 & 0.8111 & 0.8178 & **0.8185** \\ \hline \multirow{2}{*}{knee} & \(\times\)2 & 0.3647 & 0.9008 & 0.9072 & 0.9073 & 0.9054 & **0.9078** \\  & \(\times\)4 & 0.0919 & 0.7840 & **0.7908** & 0.7858 & 0.7864 & 0.7864 \\ \hline \multirow{2}{*}{head} & \(\times\)2 & 0.3126 & 0.8065 & 0.8211 & 0.8997 & 0.8075 & **0.9609** \\  & \(\times\)4 & 0.2081 & 0.6434 & 0.6336 & 0.6503 & 0.6508 & **0.6539** \\ \hline \hline \end{tabular} Note: The numbers in bold are the best results.  
\end{table} 
Table 4: SSIM values of different loss functions (K-space truncation downsampling).