## 3 Experiment
### Neutron Experiment  
The neutron experiments were carried out on a neutron imaging test station at end of the CNGB guide of the China Advanced Research Reactor (CARR) located at the China Institute of Atomic Energy. In order to simulate the neutron imaging nondestructive testing process of spent fuel, a 20 cm simulated nuclear fuel rod was used to obtain neutron projection data by using an indirect neutron CT device based on a neutron IP plate [33]. During the experiment, the operation power of CARR was 30 MW, and the neutron flux at the sample was 1 \(\times\) 10\({}^{8}\)/cm\({}^{2}\)/s with a collimation ratio L/D of approximately 100. In the experiment, the 20 cm \(\times\) 25 cm neutron IP plates were used to obtain the neutron projection images, and the imaging data were obtained by scanning the IP plates with the Typhoon FLA 7000 IP laser scanning imager. The neutron projection images of the nuclear fuel element were collected every 1\({}^{\circ}\) in the range of \([0^{\circ},180^{\circ}]\). Each neutron IP plate collected 5 projection data, and a total of 36 neutron IP plates with 180 projection data were collected. A normalized neutron projection image from one angle is shown in Figure 9a. The sinogram of an axial layer is shown in Figure 9b. The low quality of the normalized neutron projection image is due to the noise produced by gamma rays on the neutron IP plates, the inconsistency of the neutron IP plates in the experiment, and the  
Figure 8: The profile of the red line position in Figure 2b. The number of projections is (**a**) 30; (**b**) 60; (**c**) 60+. Here, 60+ indicates that Poisson noise is added to 60 projections. Figure 7: The histograms of evaluation index for reconstructed images of the circular phantom with different numbers of projections. (**a**) SSIM; (**b**) PSNR; (**c**) RMSE. Here, 60+ indicates that Poisson noise is added to 60 projections. registration error of the projection images in the angle segmentation. Since the nuclear fuel element is only close to the middle part in the projected image, the image is clipped before reconstruction to leave only the image of the nuclear fuel element. The size of the useful image is \(5000\times 200\). FBP algorithm is used to restore slice image from 180 projections, and the reconstructed image is used as a reference image to compare with the reconstructed results obtained by using other algorithms (FBP, SIRT, SIRT-TV, SIRT-WTDM, and SIRT-MWTDM) with 60 projections. The reconstructed reference image is shown in Figure 10a, and it is normalized. The reconstructed results of other algorithms are also normalized. The reconstructed results of the five algorithms are shown in Figure 10b-f. The parameters of the iterative algorithm are as follows: \(\lambda_{\text{SIRT}}=0.8\), \(\lambda_{\text{{red}}}=0.995\), \(\varphi=1\), and \(N_{\text{iter}}=100\). As for the SIRT-TV algorithm, \(\lambda_{TV}=1.0\). As for the SIRT-WTDM algorithm, \(\omega=0.00003\). As for the SIRT-MWTDM algorithm, \(\gamma=0.3\) and \(k=20\). From the reconstructed results in Figure 10b, it is observed that severe artifacts exist in this image due to the limitation of the number of projections. The interior of the reconstructed image is rougher because of noise. The SIRT algorithm provides a better reconstructed image compared with FBP, but the streak artifacts are still present as shown in Figure 10c. As shown in Figure 10d,e, a large number of artifacts are suppressed by using the SIRT-TV and SIRT-WTDM algorithms. However, the effect of the SIRT-TV and SIRT-WTDM algorithms on noise suppression is not as good as that of the SIRT-MWTDM algorithm. Visually, the SIRT-MWTDM algorithm performs better in terms of noise suppression and artifact reduction compared with the other algorithms. Moreover, the SIRT-MWTDM algorithm is superior to other methods and produces an excellent-quality image in terms of maintaining detailed structure. It preserves most structural information without any physical deformation.