# Optimizing Parameters for Enhanced Iterative Image Reconstruction Using Extended Power Divergence
## 4 Experiments
### Experimental Results  
First, we present the results of numerical experiments when the distance function is chosen as the Euclidean distance between the reconstructed image and the true image (Equation (12)). Figure 3 shows the evolutions of the parameters and the evaluation function \(g\) obtained through solving our optimization problem associated with the set in (11) for two types of phantoms. The horizontal axis represents the iterations of the optimization algorithm \(t=0,1,2,\ldots\), while the green points represent the parameters, with their values referable on the left vertical axis. The brown points show the evaluation function \(g(\lambda(t);N)\) along with its values on the right vertical axis. The algorithm stops  
Figure 1: (**a**) Disc and (**b**) modified Shepp–Logan phantom images. Figure 2: Images reconstructed from X-ray CT scanner projections using (**a**) FBP procedure and (**b**) MLEM method. when either the maximum number of iterations is reached, or the parameter changes fall below a predetermined tolerance, with the iteration count at which it stops denoted as \(T\). Regardless of the phantom type, \(\lambda(t)\) changes due to the iteration process, and \(g(\lambda(t);N)\) decreases monotonically. However, the parameter set \(\lambda(T)\) at iteration \(T\) differs by phantom type: \((0.17,3.45)\) for the disc and \((0.39,2.48)\) for the Shepp-Logan phantom. Figure 4 shows the iteration process of the evaluation function values when the initial parameter \(\lambda(0)\) and the final parameter \(\lambda(T)\) are given to the PDEM iterative system, represented by blue and red points, respectively. Since \(\lambda(0)=(1,1)\) was chosen, the blue points provide results identical to the MLEM method. The function values \(g(\lambda(0);N)\) and \(g(\lambda(T);N)\) at \(N=30\) match the values shown in Figure 3 at the initial iteration \(t=0\) and final iteration \(t=T\), respectively. Figure 5 shows the images reconstructed using MLEM and PDEM at iteration \(N\) and the corresponding subtraction images from the true values, where the parameter for PDEM is \(\lambda(T)\). The density profiles along the column direction of the images are plotted in Figure 6.  
Figure 4: Evolution of the evaluation function \(g(\lambda(0);n)\) and \(g(\lambda(T);n)\) with the number of iterations \(n\) for phantoms (**a**) disc and (**b**) Shepp–Logan (shown as blue and red iterative points, respectively). The distance function is the Euclidean distance between the reconstructed image and the true image. Figure 3: Parameters \(\gamma(t)\) and \(\alpha(t)\) (green iterative points, left axis) and the evaluation function \(g(\lambda(t);N)\) (brown iterative points, right axis) at each iteration \(t\) in the optimization process of the evaluation function for phantoms (**a**) disc and (**b**) Shepp–Logan. The distance function is the Euclidean distance between the reconstructed image and the true image. Next, we present the results of numerical experiments when the distance function is chosen as the Euclidean distance (Equation (13)), KL-divergence (Equation (14)), EPD (Equation (15)), and WEPD (Equation (17)) between forward and measured projections. Figure 7 shows the evolution of the parameters obtained from the optimization associated with the set in (11) and the transition of the evaluation function through iterations, with the graph representation following the same format as in Figure 3. In each of the four distance functions, the evolution of the evaluation function \(g(\lambda(t);N)\) decreases monotonically, demonstrating that the proposed algorithm operates as expected. Figure 8 illustrates the iterative process of the evaluation function value when the initial value \(\lambda(0)\) and the final value \(\lambda(T)\) are applied to the PDEM system.