## 3 Results and Discussion
### Comparison of Deblurring Results. The first row of Figure 4 shows the eight ground truth blur kernels. To evaluate the effectiveness of blur kernel estimation, a test image, namely \"Img21,\" was artificially blurred by the eight ground truth blur kernels, therefore eight simulated blurred images were obtained. Subsequently, these blurred images were used as the inputs of the proposed method and other methods discussed above. \begin{table}
\begin{tabular}{l l l l l l l l l l} \hline \hline \multirow{2}{*}{**PSF**} & **Number** & **(a)** & **(b)** & **(c)** & **(d)** & **(e)** & **(f)** & **(g)** & **(h)** \\  & **Size** & 19\(\times\)19 & 17\(\times\)17 & 15\(\times\)15 & 27\(\times\)27 & 13\(\times\)13 & 21\(\times\)21 & 23\(\times\)23 & 23\(\times\)23 \\ \hline
**Method** & Duration & 64.572 & 63.431 & 56.714 & 81.508 & 50.356 & 67.938 & 69.447 & 74.999 \\
**in** [35] & MSE & 0.6182 & 0.2592 & 0.2259 & 0.1062 & 0.6942 & 0.2656 & 0.1457 & 0.0975 \\ \hline
**Method** & Duration & 6.9690 & 6.9370 & 6.8580 & 7.5930 & 6.1690 & 7.0620 & 7.0930 & 7.3120 \\
**in** [36] & MSE & 0.4893 & 0.3763 & 0.3722 & 0.0977 & 0.7499 & 0.2036 & 0.0867 & 0.1339 \\ \hline
**Method** & Duration & 95.979 & 56.916 & 35.043 & 211.07 & 25.636 & 110.29 & 131.32 & 143.96 \\
**in** [37] & MSE & 0.6249 & 0.7617 & 0.2892 & 0.3221 & 0.4817 & 0.3404 & 0.1711 & 0.4252 \\ \hline
**Method** & Duration & 71.577 & 70.950 & 65.525 & 126.08 & 58.953 & 77.165 & 110.45 & 119.04 \\
**in** [38] & MSE & 0.5624 & 0.3650 & 0.1807 & 0.1364 & 0.2374 & 0.2312 & 0.1012 & 0.1525 \\ \hline
**Proposed** & Duration & 14.702 & 14.327 & 13.796 & 28.076 & 13.171 & 18.061 & 21.624 & 21.653 \\
**method** & MSE & **0.4823** & **0.1540** & **0.1024** & **0.0675** & **0.1110** & **0.1161** & **0.0627** & **0.0821** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison results of the blur kernel estimation. The cost durations are recorded in seconds, and the best results of mean square error (MSE) are shown in bold. Figure 3: Examples of the ground truth images. (**a**) Img02. “RedDoor.png”; (**b**) Img07: “Flowers.png”; (c) Img21: “Lighthouse.png.”. To evaluate the blur kernel estimation more objectively, the mean square errors (MSE) of the estimated blur kernels were calculated and are listed in Table 1. The cost durations for the deblurring methods were also recorded. Our method was implemented in MATLAB, and the comparisons were assessed using a Windows platform with an Intel Xeon E5-2620 v4 CPU (2.1 GHz, 8 cores) and 32 GB RAM. The comparison results are shown in Figure 4.  
Table 1 shows that the proposed method achieves faster convergence than most of the other methods. Because the method in [36] adopts the fast Fourier transform technique both in the kernel estimation and in the deblurring process, we estimated the blur kernel in the pixel domain directly, using the conjugate descent method. Although our estimation of the blur kernels required more time, we avoided truncation and division operations in the high-frequency domain; this effectively improved the estimation accuracy. In practice, the estimated blur kernels of our method achieved the best visual effects and achieved the lowest MSE as shown in the last row of Figure 4 and Table 1.  
In our experiments, to evaluate our method and compare it with other similar ones, we used the peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) as the full-reference image quality assessment (FRIQA) parameters, which are shown in Equations (24) and (25). The PSNR [39] is a conventional indicator that is widely employed for measuring the quality of image reconstruction:  
\[PSNR(\mathbf{x},\mathbf{y})=10\lg\frac{L^{2}}{MSE(\mathbf{x},\mathbf{y})}, \tag{24}\]  
where \(\mathbf{x}\) and \(\mathbf{y}\) represent the reference image and deblurred result, respectively, \(MSE(\mathbf{x},\mathbf{y})=\mathbf{x}-\mathbf{y}_{2}^{2}\) represents the mean square error between them, and \(L\) stands for the image dynamic range.