# Blur Kernel Estimation by Structure Sparse Prior
## 4 Experiments and Results
### Result  
In this section, several experimental evaluations are presented. The PSNR and SSIM values with various deblurring methods are shown in Tables 2 and 3, respectively. It can be seen that our proposed method can achieve higher SSIM and PSNR than other methods. Besides, Figure 8 shows the corresponding visual illustration. It is observed that our proposed method obtains better performance compared with other methods. The reason is that the proposed method takes into account the structure relationship among neighbor pixels of the input image to help alleviate the ill-posed problem. Figure 9 shows the blur kernel estimation by different methods. The proposed method achieves better blur field than the competitors.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Image** & **Image Size** & **[PERSON] [27]** & **[PERSON] [8]** & **[PERSON] [28]** & **Our** \\ \hline Image1 (church) & 800 \(\times\) 800 & 0.5884 & 0.6145 & 0.6128 & **0.6180** \\ \hline Image2 (clock) & 800 \(\times\) 800 & 0.334 & 0.2874 & 0.3872 & **0.4847** \\ \hline Image3 (backyard) & 800 \(\times\) 800 & 0.6395 & 0.6245 & 0.6463 & **0.6851** \\ \hline Image4 (roof) & 800 \(\times\) 800 & 0.4899 & 0.4748 & 0.4819 & **0.5200** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison on four images from a real-world benchmark dataset. SSIM values of the debluring images by different methods.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Image** & **Image Size** & **[PERSON] [27]** & **[PERSON] [8]** & **[PERSON] [28]** & **Our** \\ \hline Image1 (church) & 800 \(\times\) 800 & 23.05 & 22.951 & 23.031 & **23.3618** \\ \hline Image2 (clock) & 800 \(\times\) 800 & 26.002 & 28.448 & 28.448 & **28.521** \\ \hline Image3 (backyard) & 800 \(\times\) 800 & 22.1814 & 21.6318 & 22.197 & **23.3827** \\ \hline Image4 (roof) & 800 \(\times\) 800 & 18.1483 & 17.1282 & 17.6505 & **18.9445** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison on four images from a real-world benchmark dataset. PSNR values of the debluring images by different methods.  
Figure 7: SSIM values with different \(\lambda_{1}\) on the experiments.  
In experiments, the parameters should be adjusted for each test image. To verify the effectiveness of our proposed method, experiments with different the size of kernel were conducted. Figure 10 shows the SSIM values with different kernel sizes. The comparison results of different methods in regard to SSIM are shown. Figure 10 shows that our proposed method achieves the best SSIM performance most of the time under different kernel sizes. No parameters were changed except the size of the kernel. It can be seen that our proposed method has its advantage in different kernel sizes. The reason is that both the sparsity regularization and the locality constraint are incorporated to obtain less reconstruction error and preserve the structure information of the image.  
Figure 8: Experimental results with four methods: (**a**) blurred image; (**b**) [PERSON]_2008. (**c**) [PERSON]_2011; (**d**) [PERSON]_2013; and (**e**) our proposed method.  
Figure 9: Comparison of blur kernel estimation: (**a**) blurred image; (**b**) [PERSON]_2008. (**c**) [PERSON]_2011; (**d**) [PERSON]_2013; and (**e**) our proposed method.