# Multiple Optimizations-Based ESRFBN Super-Resolution Network Algorithm for MR Images
## 3 Experimental Results and Analysis
### Experiment 2: Analysis of the Convergence of Each Loss Function Index during the Training Process  
In order to enable the network to converge better during the training process and avoid falling into the local optimal solution, the cascaded loss function L1+MS-SSIM uses parameter \(\alpha\) to balance the PSNR index and the SSIM index. As can be seen from the training convergence curve of the ESRFBN network in Figure 4, it began to converge before 80 epochs. Uncertain factors in the calculation of loss function were increased by adjusting the attenuation of the learning rate and parameter \(\alpha\), so as to avoid falling into the local optimal solution. The attenuation of parameter \(\alpha\) is shown in Figure 4, which is attenuated by half at the 90 th epoch, 120 th epoch and 190 th epoch, respectively. In this section, in order to reflect the impact of parameter \(\alpha\)'s attenuation on the training process better, the difference between the evaluation indexes of the cascaded loss function (Mix) and other loss functions during the training process is used for characterization. Figure 5 shows the curve of the number of iterations and the difference in PSNR during the training of each loss function, and Figure 6 shows the curve of the number of iterations and the difference in the SSIM during the training of each loss function. It can be seen from the figure that at 90 epoch and 120 epoch, the difference between the Mix loss function and other loss functions will have obvious vibrations. This is because in the Mix loss function,  
Figure 4: Attenuation of parameter \(\alpha\). Figure 3: Knee: the super-resolution graph of each loss function of the ESRFBN network at scale 4.  
the parameter \(\alpha\) attenuated and the loss function curve oscillates, resulting in lower PSNR and SSIM values calculated by the model. However, the difference tends to stabilize after rising in the subsequent process. This shows that ESRFBN has a strong convergence ability. On the other hand, it shows that during the training process, the learning rate attenuation strategy can prevent the network from falling into the local optimal solution, so that the network model obtained finally has a better super-resolution effect. In order to improve the PSRN and SSIM indexes of MR super-resolution, this section proposes a method based on PSNR-SSIM joint loss function cascade optimization. In order to verify the effectiveness of the proposed method, four experiments were carried out on the data sets generated by the two modes. Experiment 1 proves that the L1+MS_SSIM cascaded loss function can obtain the optimal super-resolution effect, which proves the effectiveness of the optimization of the cascading loss function. This is mainly because the cascading loss function combines the advantages of the L1 loss function which can keep the brightness and color unchanged and the MS_SSIM loss function which can retain the contrast and is better than other loss functions in the high frequency area, so that the cascading loss function has the best  
Figure 5: The scale of the knee part is 4: The PSNR difference between the training process of the Mix loss function and other loss functions. Figure 6: The scale of the knee is 4: The difference between the training process of the Mix loss function and other loss functions SSIM. characteristics of the two loss functions. The cascade loss function optimization enables the ESRFBN network to obtain a better super-resolution effect of MR images. Through Experiment 2, it can be proved that parameter attenuation can make the difference between the Mix loss function and other loss functions vibrate significantly, so as to avoid the network falling into the local optimal solution and make the obtained network model have better super-resolution effect. At the same time, it shows that the ESRFBN network has strong convergence ability, which can make deep network converge quickly in the training process and reduce the learning difficulty of network.