# A Graduated Non-Convexity Technique for Dealing Large Point Spread Functions
## 5 Experimental Results
Again, one can immediately see that the implicit use of line elements improves qualitatively and quantitatively the quality of the reconstructions. In the third set of experiments, we consider a Gaussian shape PSF of standard deviation \(\widetilde{\sigma}=10.25\), and we add to the blurred data a Gaussian noise of variance \(\widehat{\sigma}^{2}=4\). We present the reconstructions obtained by CATILED and E-CATILED for the two test images in Figures 8 and 9. Here, we pose \(\widehat{\lambda}=0.01\), \(\widehat{\alpha}=0.1\), and \(\widehat{\varepsilon}=0.1\). Figure 5: (**a**) First ideal image; (**b**) second ideal image. Figure 6: (**a**) Blurred data; (**b**) CATILED reconstruction (MSE = 31.4166); (**c**) E-CATILED reconstruction (MSE = 31.3254); (**d**) Tikhonov reconstruction (MSE = 49.0748). Figure 7: (**a**) Blurred data; (**b**) CATILED reconstruction (MSE = 79.5116); (**c**) E-CATILED reconstruction (MSE = 79.6245). In Table 5, we report the errors, in terms of MSE, of the reconstructions obtained by CATILED and E-CATILED. Thus, these experiments show that the results of the two algorithms are equivalent in both quantitative and visual terms. Let us now consider the real data presented in Figure 10a. Such an image is an RGB color image. A color image version of CATILED is presented in [53]. However, in this case, in the blurred image, there does not appear to be any loss of saturation of the original colors. Thus, we can reconstruct each color component separately. We first assume each channel has a PFS with standard deviation \(\widetilde{\sigma}=5\). The reconstructions obtained by CATILED and E-CATILED are in Figure 10b,c, respectively, and the MSE between the two reconstructions is equal to 0.1320. Then, we consider a PFS with \(\widetilde{\sigma}=7\), and the relative results are in Figure 10d,e. Here, the MSE between the two reconstructions is 0.2615. We set for both cases \(\widehat{\lambda}=0.05\), \(\widehat{\sigma}=1\), and \(\widehat{\epsilon}=1\). Again, the two algorithms yield qualitatively similar results. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Figure** & **CATILED** & **E-CATILED** \\ \hline Figure 5 & 18.6743 & 18.6591 \\ \hline Figure 6 & 31.4166 & 31.3254 \\ \hline Figure 7 & 79.5116 & 79.6245 \\ \hline Figure 8 & 76.7959 & 76.7008 \\ \hline Figure 9 & 120.4875 & 120.4984 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mean squared error of the reconstructions. Figure 8: (a) Blurred data; (b) CATILED reconstruction (MSE = 76.7959); (c) E-CATILED reconstruction (MSE = 76.7008). Figure 9: (a) Blurred data; (b) CATILED reconstruction (MSE = 120.4875); (c) E-CATILED reconstruction (MSE = 120.4984). Finally, in Table 6, we report the ratios between the calculation times of E-CATILED and CATILED. Note here that the average computation time of the CATILED algorithm was about 96.35 min. The average computation time of the E-CATILED algorithm can be easily derived from the ratios given in Table 6. Thus, in our experimental results, using E-CATILED, we have an average computational cost gain of 22.01%. It is thus evident that the use of E-CATILED is more cost-effective than CATILED in terms of computational time by not affecting the quality of the reconstruction obtained.