## 3 Experiments and Results
### Experimental Results
#### 3.4.2 Comparison of Different Algorithms  
In order to compare with MPSR, spline interpolation algorithm (SPLINE), adaptive regularization algorithm (MAP), SRCNN and sub-pixel convolution-based reconstruction algorithm (ESPCN) are also applied in the experiment. Eight images in the test set are selected to display the data. The specific images are shown in Figure 7.  
Figure 6: (a) Comparison of the objective functions of a single regular item and double regular items. (b) Comparison of PSNR values before and after algorithm improvement. The PSNR and SSIM values obtained from reconstructed images using different algorithms are listed in Tables 3 and 4. In order to evaluate the effect more intuitively, the data in Tables 3 and 4 are averaged and plotted in Figure 8. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \begin{tabular}{c} **Metric** \\ **Parameters** \\ \end{tabular} & \
\begin{tabular}{c} **Number** \\ **Number** \\ \end{tabular} &
\begin{tabular}{c} **Image** \\ **Pixel** \\ \end{tabular} & **SPLINE** & **MAP** & **SRCNN** & **ESPCN** & **MPSR** \\ \hline \multirow{9}{*}{SSIM} & 1 & 320 * 240 & 0.9113 & 0.9215 & 0.9398 & 0.9429 & 0.9516 \\  & 2 & 320 * 240 & 0.7518 & 0.7875 & 0.8315 & 0.8457 & 0.8804 \\  & 3 & 320 * 240 & 0.8779 & 0.8925 & 0.9023 & 0.9194 & 0.9365 \\  & 4 & 320 * 240 & 0.9594 & 0.9617 & 0.9645 & 0.9690 & 0.9736 \\  & 5 & 320 * 240 & 0.9593 & 0.9625 & 0.9659 & 0.9678 & 0.9702 \\  & 6 & 320 * 240 & 0.9175 & 0.9223 & 0.9290 & 0.9360 & 0.9436 \\  & 7 & 320 * 240 & 0.8099 & 0.8340 & 0.8661 & 0.8782 & 0.9059 \\  & 8 & 320 * 240 & 0.8334 & 0.8542 & 0.8784 & 0.8889 & 0.9144 \\ \hline \end{tabular}
\end{table} 
Table 4: SSIM values of different algorithms. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \begin{tabular}{c} **Metric** \\ **Parameters** \\ \end{tabular} & \
\begin{tabular}{c} **Number** \\ **Number** \\ \end{tabular} &
\begin{tabular}{c} **Image** \\ **Pixel** \\ \end{tabular} & **SPLINE** & **MAP** & **SRCNN** & **ESPCN** & **MPSR** \\ \hline \multirow{9}{*}{PSNR (dB)} & 1 & 320 * 240 & 34.0800 & 35.1562 & 36.9908 & 37.0787 & 38.0546 \\  & 2 & 320 * 240 & 23.6019 & 24.5066 & 25.9310 & 25.9588 & 27.5505 \\  & 3 & 320 * 240 & 31.3120 & 32.2794 & 33.2204 & 33.8099 & 35.0086 \\  & 4 & 320 * 240 & 31.7600 & 32.7605 & 33.0185 & 33.6165 & 36.7969 \\  & 5 & 320 * 240 & 31.8201 & 32.2924 & 33.3726 & 33.6970 & 35.8422 \\  & 6 & 320 * 240 & 30.8223 & 31.2468 & 32.1141 & 32.6161 & 33.7191 \\  & 7 & 320 * 240 & 31.0702 & 31.9873 & 33.3658 & 33.7443 & 34.9114 \\  & 8 & 320 * 240 & 29.8001 & 30.8034 & 32.1989 & 32.5128 & 34.1559 \\ \hline \end{tabular}
\end{table} 
Table 3: PSNR values of different algorithms. Figure 7: Experimental images. The abscissa of Figure 8a is the algorithm name, and the ordinate is the PSNR values obtained by reconstructing the image with different algorithms. From Figure 8a, it can be seen that the SPLINE algorithm has the worst effect, the mean value of PSNR after reconstruction is only 30.5 dB, and the traditional regularization algorithm MAP is not ideal. At present, the popular algorithm based on deep learning has a better reconstruction effect than the traditional algorithm, but MPSR proposed in this paper has the best effect. It can be seen from Figure 8a that the PSNR values calculated by this algorithm is about 4 dB higher than that of SPLINE interpolation algorithm, about 2 dB higher than that of SRCNN algorithm, and about 1 dB higher than that of ESPCN algorithm. The abscissa of Figure 8b is the algorithm name, and the ordinate is the SSIM value obtained by reconstructing the image with different algorithms. Compared with the trend of PSNR, spline algorithm has the worst effect. The mean value of SSIM after reconstruction is less than 0.88, while the mean value of SSIM of MPSR is nearly 0.94, which is nearly 0.03 more than that of SRCNN algorithm and 0.02 more than that of ESPCN algorithm. The effect of the reconstructed images is as in Figure 9.  
Figure 8: (**a**) Means of PSNR values of different algorithms.