# Super-Resolution Reconstruction of an Array Lidar Range Profile
## 3 Experimental Results
### Dataset Experiment and Result Analysis
In this experiment, the number of iterations of POCS was set to \(5\), and the Gaussian model was used to simulate the PSF. The number of layers of the Gaussian image pyramid used in this paper was \(3\). Figures 3 and 4 are the \(400\%\) super-resolution reconstruction effect diagram, and Tables 1 and 2 are the evaluation index results of different algorithms under different magnifications. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**AG**} & \multicolumn{3}{c}{**ES**} & \multicolumn{3}{c}{**Time/ms**} \\ \cline{2-10}  & \(\times\)**2** & \(\times\)**4** & \(\times\)**8** & \(\times\)**2** & \(\times\)**4** & \(\times\)**8** & \(\times\)**2** & \(\times\)**4** & \(\times\)**8** \\ \hline Bilinear & 0.98 & 0.94 & 0.86 & 10.87 & 10.50 & 9.69 & 13.1 & 14.2 & 15.4 \\ Bicubic & 1.25 & 1.04 & 0.91 & 12.70 & 11.10 & 9.93 & 13.7 & 15.1 & 16.1 \\ POCS & 1.42 & 1.10 & 0.95 & 13.98 & 11.37 & 10.29 & 34.3 & 41.6 & 49.8 \\ POCS [17] & 1.53 & 1.15 & 0.99 & 15.02 & 11.95 & 10.76 & 43.2 & 48.4 & 53.3 \\ POCS with LK & 1.57 & 1.17 & 1.05 & 14.93 & 11.89 & 10.73 & 45.7 & 51.2 & 57.6 \\ POCS with Gradient & 1.41 & 1.09 & 0.96 & 15.21 & 12.03 & 11.13 & 41.4 & 46.2 & 51.1 \\ Proposed & 1.58 & 1.19 & 1.05 & 15.42 & 12.32 & 11.21 & 47.3 & 53.1 & 59.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the evaluation indicators of the sofa range profiles under different magnifications. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**PSNR**} & \multicolumn{3}{c}{**SSIM**} \\ \cline{2-7}  & \(\times\)**2** & \(\times\)**4** & \(\times\)**8** & \(\times\)**2** & \(\times\)**4** & \(\times\)**8** \\ \hline Bilinear & 22.4767 & 19.6141 & 17.4205 & 0.8126 & 0.7174 & 0.6017 \\ Bicubic & 22.6498 & 19.754 & 17.6544 & 0.7889 & 0.6707 & 0.5203 \\ POCS & 24.4371 & 22.2587 & 18.2147 & 0.8317 & 0.7752 & 0.6932 \\ POCS [17] & 25.7124 & 23.7412 & 18.8253 & 0.8617 & 0.7984 & 0.7184 \\ POCS with LK & 25.5834 & 23.7368 & 18.8865 & 0.8543 & 0.7897 & 0.7032 \\ POCS with Gradient & 24.9758 & 22.8907 & 18.8356 & 0.8412 & 0.7834 & 0.7015 \\ Proposed & 26.1342 & 24.0297 & 18.8793 & 0.8832 & 0.8084 & 0.7217 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the PSNR and SSIM of the sofa range profiles under different magnifications. Figure 3: Super-resolution rendering of the sofa range profile with (**a**) the original sofa range profile; (**b**) bilinear sofa range profile; (**c**) bicubic sofa range profile; (**d**) POCS sofa range profile; (**e**) POCS [17]; sofa range profile; (**f**) POCS with the LK sofa range profile; (**g**) POCS with gradient sofa range profile; and (**h**) the proposed sofa range profile. The sofa range profile in the dataset that can effectively distinguish the target edge from the background was selected to verify the effectiveness of the proposed algorithm. At the same time, ablation experiments were added to verify the effectiveness of the introduced LK optical flow method and gradient constraint, where POCS + LK means that the LK optical flow method is introduced to replace the traditional block matching method in POCS motion registration and POCS + Gradient indicates that gradient constraint is introduced in POCS. Figure 3a shows the original range profile; Figure 3b,c represent the range profiles of 400% upsampling bilinear interpolation and bicubic interpolation after 1/4 downsampling, respectively; Figure 3d-h, respectively, represent the 400% upsampling range profile reconstructed by using POCS after 1/4 downsampling and according to POCS, POCS + LK, and POCS + Gradient reproduced in reference [17] and the method proposed in the paper. As it can be seen from Figure 3, the details at the border of the sofa in Figure 3b are fuzzy and the edge is not sharp enough; Figure 3c is clearer than Figure 3b in terms of image details, but it can be seen from the local enlarged image of Figure 3c that the edge details at the division of sofa and background are not obvious.