# A Rigid Motion Artifact Reduction Method for CT Based on Blind Deconvolution
## 4 Discussion  
The performance of the proposed method was verified by using a modified 3D Shepp-Logan phantom, a head phantom, and patient scan. In numerical phantom experiments, the proposed method produced higher quality images for the case of slight motion than the other three considered approaches. As illustrated in Figure 4a,b, the images included severe motion artifacts over the whole image, and thereby inner structures and the skull were noticeably distorted. In Figure 4c,d the majority of distortions were eliminated. But many intensity oscillations appeared inside the phantom (see Figure 4c). The proposed method yielded an appreciable improvement on all metrics, reducing RMSE by about 30% and increasing CC and MSSIM by about 14% and 19%, respectively, compared to the RL-OSEM method (see Table 1). However, the proposed method did not perform well in cases of large motion, such as that of Figure 3b. Since the OSEM reconstruction was corrupted severely, these motion artifacts were too severe to be corrected by the proposed method (see Figure 5d). Therefore, a limitation of the method is that the proposed method usually did not perform well when the amplitude of the rotations was more than 30\({}^{\circ}\) and the amplitude of the translations was more than 30 mm. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Metric** & **RMSE(HU)** & **CC** & **MSSIM** \\ \hline \multirow{2}{*}{Uncorrected} & Mean & 231.4553 & 0.5182 & 0.3996 \\  & Standard deviation & 80.6443 & 0.0848 & 0.1043 \\ \multirow{2}{*}{OSEM-BD} & Mean & 223.8676 & 0.5285 & 0.4069 \\  & Standard deviation & 77.5233 & 0.0838 & 0.1028 \\ \multirow{2}{*}{RL-OSEM} & Mean & 126.2337 & 0.8236 & 0.7440 \\  & Standard deviation & 35.2356 & 0.0590 & 0.0635 \\ \multirow{2}{*}{BD-OSEM} & Mean & 88.4645 & 0.9497 & 0.8976 \\  & Standard deviation & 22.6645 & 0.0301 & 0.0394 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Evaluation of motion artifact reduction performance on patient scan. Figure 8: Comparison of the selected slice of reconstructed images for patient scan: (**a**) Reconstructed image without motion correction; (**b**) image reconstructed by OSEM-BD; (**c**) image reconstructed by RL-OSEM; (**d**) image reconstructed by the proposed method; (**e**) repeated scan. In head phantom experiments, the reconstructed images showed marked improvement when the proposed method was applied. As shown in Figure 6a,b the reconstructed images exhibited severe motion artifacts and distorted image quality. And the image reconstructed by the RL-OSEM method still had artifacts and its edge appeared thinner than the true image (see Figures 6c and 7c). All the metrics also suggested improvement motion correction performance on the proposed method. The RMSE of the proposed method was the smallest and reduced by about 27% compared to the RL-OSEM method; the CC and MSSIM of the proposed method were the greatest and increased by about 15% and 20%, respectively, compared to the RL-OSEM method (see Table 3). Comparative results on numerical phantom and head phantom show that the OSEM-BD method can eliminate noise but not reduce motion artifacts. The BD-OSEM method can effectively reduce motion artifacts and the noise in flat regions as well as preserve the edge and detailed information. In patient scan experiments, the reconstructed images, even with motion correction, provided severe motion artifacts (see Figure 8b,c). Most of the motion artifacts in the reconstructed image were eliminated after the motion correction by the proposed method (see Figure 8d). The RMSE of the proposed method can reduce by about 30%, compared to the RL-OSEM method; the CC and MSSIM of the proposed method can increase by about 15% and 21%, respectively, compared to the RL-OSEM method (see Table 4). The computation will take a long time since there are a large number of CT views in clinical scans.