## 3 Experiment
### Neutron Experiment
The RMSE, PSNR, and SSIM are used to carry out quantitative analysis on the reconstructed results obtained by using the five algorithms for 60 projections. The results are shown in Figure 11. It can be seen from Figure 11 that the RMSE value of the image reconstructed by SIRT-MWTDM algorithm is the smallest, which indicates the minimum error between the reconstructed image and the reference image. The PSNR value of the image reconstructed by using SIRT-MWTDM algorithm is the largest, which indicates that the reconstructed image is smoother and the algorithm has a stronger ability to suppress noise. The SSIM value of the reconstructed image obtained by SIRT-MWTDM algorithm is the largest, which indicates that the reconstructed image retains more structural information. We also plot the profile in Figure 12, which shows the profile marked by the horizontal yellow line in Figure 10a. By comparison, the SIRT-MWTDM algorithm has advantages in that the profile is much closer to the reconstructed results obtained by using the FBP algorithm and 180 projections. In conclusion, real neutron reconstructed images indicate that our algorithm has good performance in artifact reduction and noise suppression. Figure 9: Neutron projection image and sinogram. (**a**) A neutron projection image of the nuclear fuel element from one angular view. (**b**) A sinogram of an axial layer. AVIZO software was used to measure the area of the high-brightness substance indicated by the red arrow in Figure 10, and the measurement results are shown in Table 1. As can be seen from Table 1, the area measured from Figure 10 is closest to that of the reference image Figure 10a. The reconstruction of the nuclear fuel element was performed from all axial positions by using the proposed algorithm. A three-dimensional (3D) representation of several series of slices is shown in Figure 13. TheAVIZO software was used to generate the 3D representation. To show the internal structure more clearly, the 3D image is displayed in color. Some of the pixels in the 3D image of the nuclear fuel element were dissected out to see the internal structure. The boundary of the nuclear fuel element and the vertical hole can be seen clearly in the diagram. The different colors of the image represent different types of substances. The red pixels represent uranium, which has a high neutron attenuation  
Figure 11: The histograms of evaluation index for reconstructed neutron images from 60 projections. (**a**) RMSE; (**b**) PSNR; (**c**) SSIM. Figure 10: Reconstructed results obtained by using the different algorithms with the display windows set to [0, 1]. (**a**) Reconstructed results obtained by using FBP algorithm and 180 views; (**b**) reconstructed results obtained by using FBP algorithm and 60 views; (**c**) reconstructed results obtained by using SIRT algorithm and 60 views; (**d**) reconstructed results obtained by using SIRT-TV algorithm and 60 views; (**e**) reconstructed results obtained by using SIRT-WTDM algorithm and 60 views; (**f**) reconstructed results obtained by using SIRT-MWTDM algorithm and 60 views. we need to continuously adjust the values of these two parameters until a satisfactory result is obtained, which would be the shortcoming of the proposed algorithm in this paper. For the reconstruction of new samples, it may take some time to adjust the parameters \(\gamma\) and \(k\). The other algorithms used in the article use fewer parameters than the proposed algorithm. Therefore, it takes less time for other algorithms to adjust parameters than the proposed algorithm. We believe it is worthwhile to spend some time adjusting the parameters of the proposed algorithm to achieve high-quality reconstructed images. We compare the convergence speed of the SIRT-MWTDM method with other algorithms. The RMSE and SSIM curves of the reconstruction process in Figure 3 for 30 Shepp-Logan projections are shown in Figure 14. The RMSE curve for each iteration is shown in Figure 14a.