# Optimizing Parameters for Enhanced Iterative Image Reconstruction Using Extended Power Divergence
## 4 Experiments
### Experimental Results
The reconstructed images at iteration \(N\) are shown in Figure 9. Tables 1 and 2 summarize the parameter values \(\lambda(T)\), SSIM, and standard deviation (for the disc phantom) between the reconstructed images and the true images for each distance function when the optimization of the evaluation function reaches iteration \(T\). Figure 5: Images reconstructed using MLEM and PDEM (**top**) and corresponding subtraction images (**bottom**) defined by the distance function for phantoms (**a**) disc and (**b**) Shepp–Logan. The distance function is the Euclidean distance between the reconstructed image and the true image. Figure 6: The density profile along the column direction (\(\ell=1,2,\ldots,128\)), fixed at the 51 st row (\(L=6,400\)), for images reconstructed using MLEM and PDEM for phantoms (**a**) disc and (**b**) Shepp–Logan. The black, blue, and red lines represent the true values, MLEM, and PDEM, respectively. The distance function is the Euclidean distance between the reconstructed image and the true image. Figure 8: Changes in the evaluation function \(g(\lambda(0);n)\) and \(g(\lambda(T);n)\) with the number of iterations \(n\) (shown as blue and red iterative points, respectively) for a disc phantom. The distance function is the (**a**) Euclidean distance, (**b**) KL-divergence, (**c**) EPD, and (**d**) WEPD between forward and measured projections. Figure 2:0 The parameters \(\gamma(t)\) and \(\alpha(t)\) (green iterative points, left axis) and the evaluation function \(g(\lambda(t);N)\) (brown iterative points, right axis) during each iteration \(t\) in the optimization process for a disc phantom. The distance function is the (**a**) Euclidean distance, (**b**) KL-divergence, (**c**) EPD, and (**d**) WEPD between forward and measured projections. Finally, we present the results of the physical experiment. Figure 10 plots the optimization process and the transition of the evaluation function when the proposed method is applied to projections obtained from the X-ray CT scanner, using WEPD as the distance function between forward and measured projections as an example. The reconstructed images and density profiles, including those for other distance functions, are shown in Figures 11 and 12, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Dist. Func.** & \(\gamma\) & \(\alpha\) & **SSIM** & **Std. Dev.** \\ \hline \multirow{2}{*}{MLEM} & — & 1 & 1 & 0.816 & 0.111 \\ \cline{2-6}  & (a) & 1.219 & 0.744 & 0.813 & 0.122 \\ \cline{2-6}  & (b) & 0.957 & 1.39 & 0.798 & 0.118 \\ \cline{2-6}  & (c) & 0.139 & 9.21 & 0.983 & 0.0719 \\ \cline{2-6}  & (d) & 0.143 & 9.17 & 0.982 & 0.0727 \\ \cline{2-6}  & (e) & 0.166 & 3.45 & 0.981 & 0.0517 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance evaluation of images reconstructed using MLEM and PDEM (with parameters \(\lambda(T)\)) for disc phantom. The distance functions are (a) Euclidean distance, (b) KL-divergence, (c) EPD, and (d) WEPD between forward and measured projections, and (e) Euclidean distance between the reconstructed and true images. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Dist. Func.** & \(\gamma\) & \(\alpha\) & **SSIM** \\ \hline \multirow{2}{*}{MLEM} & — & 1 & 1 & 0.900 \\ \cline{2-5}  & (a) & 1.34 & 0.764 & 0.889 \\ \cline{2-5}  & (b) & 0.959 & 1.40 & 0.889 \\ \cline{2-5}  & (c) & 0.156 & 8.31 & 0.928 \\ \cline{2-5}  & (d) & 0.169 & 7.86 & 0.932 \\ \cline{2-5}  & (e) & 0.393 & 2.48 & 0.939 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance evaluation of images reconstructed using MLEM and PDEM (with parameters \(\lambda(T)\)) for Shepp–Logan phantom. The distance functions are (a) Euclidean distance, (b) KL-divergence, (c) EPD, and (d) WEPD between forward and measured projections, and (e) Euclidean distance between the reconstructed and true images. Figure 9: Images reconstructed using PDEM (with parameters \(\lambda(T)\)) **(top)** and the corresponding subtraction images (**bottom**) for a disc phantom.