## 3 Experiment
### Simulation Experiment
#### 3.2.1. _S_epp-Logan_ Phantom  
Four reconstruction algorithms, FBP, SIRT, SIRT-TV, and SIRT-WTDM, are used for comparison with the reconstructed results obtained by using the SIRT-MWTDM algorithm in this paper. The calculation process of the SIRT-TV algorithm includes one SIRT and one TV. We can obtain the reconstructed image when the set number of iterations is reached. To make a reasonable and fair comparison of the four algorithms, we set the parameters of the algorithms as follows: \(\lambda_{\text{SIRT}}=1.8\), \(\lambda_{rd}=0.995\), \(\varphi=1\), and \(N_{\text{iter}}=600\). As for the SIRT-TV algorithm, \(\lambda_{TV}=1.0\). \(\lambda_{TV}\) is a positive factor of TV. As for the SIRT-WTDM algorithm, \(\omega=0.00035\). As for the SIRT-MWTDM algorithm, \(\gamma=0.6\) and \(k=100\). The reconstructed images with different numbers of projections obtained by using the five reconstruction algorithms are shown in Figure 3.  
From Figure 3, we can see that as the number of projections increases, the clarity and smoothness of the images reconstructed by the five algorithms are gradually improved, and the quality of reconstructed images is significantly improved when there is no noise in the projections. However, compared with the other four algorithms, there are obvious artifacts in the image reconstructed by using the FBP algorithm. The reconstructed images of SIRT, SIRT-TV, and SIRT-WTDM are smoother than that of FBP algorithm from 30 projections. The edges of the image reconstructed by using the SIRT-MWTDM algorithm are sharper than those of other algorithms. The boundaries of the three ellipses at the bottom of the image reconstructed by using SIRT-MWTDM algorithm are clearer than those of other algorithms. For 60 noise-free projections with 600 iterations, the image reconstructed by using SIRT-MWTDM method almost has no difference \(f\) the original image in visual effect. For 60 noisy projections, it can be seen that the image reconstructed by SIRT-MWTDM is  
Figure 2: Simulated phantom. (**a**) Shepp–Logan phantom; (**b**) circular phantom. The display windows of two phantoms are set to \([0,255]\). less noisy. The intervals among the three ellipsoids are more obvious at the bottom of the reconstructed image. SSIM, PSNR, and RMSE are calculated for the images reconstructed by using the five algorithms with different numbers of projections, and the results are shown in Figure 4. We first analyze the evaluation index of the image reconstructed by using noise-free projections. As can be seen from the SSIM histogram in Figure 4a, as the number of projections increases, the SSIM values of the image reconstructed by using each algorithm are improved. In the case of the same number of projections, the SIRT-MWTDM algorithm has the highest SSIM for reconstructed images. The SSIM value of the image reconstructed by the SIRT-MWTDM algorithm is 0.9878 for 30 projections, which also indicates that the proposed algorithm is superior to other algorithms in retaining structural information of the reconstructed image. As can be seen from the PSNR histogram in Figure 4b, PSNR and SSIM have similar characteristics. As the number of projections increases, the PSNR of the images reconstructed by using each algorithm is also improved. The PSNR value of the image reconstructed by the SIRT-MWTDM algorithm is the largest with the same number of projections. The PSNR value of the image reconstructed by using the SIRT-MWTDM algorithm is 34.3259 for 30 projections, which indicates that the proposed algorithm is superior to other algorithms in noise reduction. As can be seen from the RMSE histogram in Figure 4c, the variation trend of RMSE is opposite to that of SSIM and PSNR. The RMSE values of the image reconstructed by using SIRT-MWTDM are the smallest with the same  
Figure 3: Reconstructed results of the Shepp–Logan phantom obtained by using different algorithms with different numbers of projections. Images from left to right show reconstructed results from 30, 60, and 60+ projections, respectively.