# Image Deblurring Based on Convex Non-Convex Sparse Regularization and Plug-and-Play Algorithm
## 5 Numerical Experiment
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(\
u\)} & \multirow{2}{*}{**Method**} & \multirow{2}{*}{**CPU Time**} & \multicolumn{8}{c}{**Blur kernel**} \\ \cline{3-10}  & & & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \multirow{4}{*}{0.01} & IRCNN & 24.32 & 32.68 & 32.20 & 31.35 & 32.17 & 32.24 & 32.65 & 31.46 & 31.42 \\  & DPIR & 25.93 & 33.61 & 33.18 & 32.95 & 33.01 & 34.03 & 34.29 & 33.02 & 32.70 \\  & GS-PnP & 26.60 & 33.47 & 32.97 & 32.83 & 32.79 & 34.01 & 34.19 & 32.88 & 32.49 \\  & PnP-FBS-CNC & **24.28** & **33.98** & **33.56** & **33.37** & **33.45** & **34.48** & **34.69** & **33.38** & **33.16** \\ \hline \multirow{4}{*}{0.03} & IRCNN & **27.58** & 29.25 & 28.81 & 28.84 & 28.56 & 29.72 & 29.61 & 28.82 & 28.49 \\  & DPIR & 28.15 & 29.31 & 28.98 & 29.13 & 28.68 & 30.14 & 30.17 & 29.25 & 28.82 \\  & GS-PnP & 30.57 & 29.16 & 28.82 & 29.13 & 28.54 & 30.26 & 30.15 & 29.26 & 28.86 \\  & PnP-FBS-CNC & 28.07 & **29.81** & **29.49** & **29.68** & **29.25** & **30.67** & **30.66** & **29.77** & **29.37** \\ \hline \multirow{4}{*}{0.05} & IRCNN & **30.24** & 26.92 & 26.67 & 27.16 & 26.29 & 28.22 & 28.00 & 27.14 & 26.75 \\  & DPIR & 31.52 & 27.45 & 27.26 & 27.67 & 26.91 & 28.55 & 28.27 & 27.71 & 27.23 \\ \cline{1-1}  & GS-PnP & 32.67 & 27.38 & 27.21 & 27.63 & 26.92 & 28.63 & 28.36 & 27.74 & 27.33 \\ \cline{1-1}  & PnP-FBS-CNC & 31.19 & **28.03** & **27.76** & **28.22** & **27.51** & **29.12** & **28.95** & **28.24** & **27.84** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Average PSNR performance (dB) and CPU time of image deblurring on the CBSD68 dataset. The best results are highlighted in bold. Figure 1: Blur kernels. We next assess the deblurring performance of these methods in terms of visual aspects. As indicated in Table 1, the optimal PSNR numerical performance is achieved when the noise level is 0.01. Therefore, we select the images with this noise level to examine the deblurring visual effect. Additionally, considering the extensive number of images available, we selectively choose three groups of images as exemplars to observe their respective deblurring effects. Meanwhile, we select different blur kernels for each of these three groups of images: kernel 1 with size \(19\times 19\), kernel 3 with size \(15\times 15\), and kernel 5 with size \(13\times 13\). The corresponding visual comparison results for each method are illustrated in Figures 2-4. After examining these images, it can be concluded that the quality of the images produced by IRCNN is comparatively inferior to those obtained by other methods. This distinction can be readily observed by comparing the water region of each image in Figure 2 and the blue sky region of each image in Figures 3 and 4. We observe that the PnP-FBS-CNC method yields an image that is more closely aligned with the clean image and exhibits superior clarity in processing fine textures. The PSNR value displayed in the image indicates that PnP-FBS-CNC outperforms other methods in terms of deblurring performance. In conclusion, the above performance demonstrates the superiority of the proposed algorithm for image deblurring, thereby strongly validating its effectiveness. Figure 4: Image deblurring results of different methods with blur kernel 5. Two local images in the red box are enlarged. Figure 3: Image deblurring results of different methods with blur kernel 3. Two local images in the red box are enlarged.