# A Rigid Motion Artifact Reduction Method for CT Based on Blind Deconvolution
## 3 Results
### Head Phantom Experiments  
In the following simulations, the proposed method was verified on head phantom. A selected slice of head phantom was shown in Figure 2b. The sinogram was acquired from head phantom with motion and noise that were the same as the Shepp-Logan phantom experiments. The head CT image was acquired from a GE Hi-Speed multi-slice CT scanner. A total of 720 views were uniformly selected over a 360\({}^{\circ}\) range under 150 mA \(X\)-ray tube current and 120 kVp. The display window was [\(-5\) HU, 75 HU]. All of the reconstructed images (\(512\times 512\) pixels) were reconstructed by the OSEM method  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Metric** & **RMSE (HU) 1** & **CC 2** & **MSSIM 3** \\ \hline \multirow{3}{*}{OSEM} & Mean & 164.3943 & 0.6474 & 0.3206 \\  & Standard deviation & 30.2477 & 0.0614 & 0.0723 \\  & Mean & 161.4823 & 0.7166 & 0.6678 \\ \multirow{3}{*}{OSEM-BD} & Standard deviation & 26.2257 & 0.0603 & 0.0714 \\  & Mean & 95.2396 & 0.8213 & 0.7722 \\ \multirow{3}{*}{RL-OSEM} & Standard deviation & 10.1925 & 0.0592 & 0.0579 \\  & Mean & 72.2313 & 0.9378 & 0.9188 \\ \multirow{3}{*}{BD-OSEM} & Standard deviation & 7.6535 & 0.0315 & 0.0379 \\ \hline \hline \end{tabular} \({}^{1}\) Root-mean-square error (RMSE); 2 Pearson correlation coefficient (CC); 3 Mean structural similarity (MSSIM).  
\end{table}
Table 1: Evaluation of motion artifact reduction performance on Shepp–Logan phantom with slight motion.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Metric** & **RMSE (HU)** & **CC** & **MSSIM** \\ \hline \multirow{3}{*}{OSEM} & Mean & 582.7321 & 0.3867 & 0.2184 \\  & Standard deviation & 97.3525 & 0.0911 & 0.1068 \\  & Mean & 512.6562 & 0.4080 & 0.2517 \\ \multirow{3}{*}{OSEM-BD} & Standard deviation & 90.5623 & 0.0893 & 0.1049 \\  & Mean & 309.0913 & 0.5058 & 0.3522 \\ \multirow{3}{*}{RL-OSEM} & Standard deviation & 70.1526 & 0.0682 & 0.0778 \\  & Mean & 198.3918 & 0.5844 & 0.4248 \\ \multirow{3}{*}{BD-OSEM} & Standard deviation & 50.2433 & 0.0515 & 0.0618 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Evaluation of motion artifact reduction performance on Shepp–Logan phantom with large motion.  
Figure 5: Comparison of the 128 th slice of 3D reconstructed images for large motion: (**a**) Image reconstructed by OSEM; (**b**) image reconstructed by OSEM-BD; (**c**) image reconstructed by RL-OSEM; (**d**) image reconstructed by the proposed method.  
with three iterations and 30 subsets. BD-iterations were stopped at the sixth iteration. The other experimental parameters were set the same as those of the Shepp-Logan phantom experiments.  
Figure 6 shows the selected slice of reconstructed images obtained by using OSEM, OSEM-BD, RL-OSEM, and the proposed method. To view the texture of reconstructed images more clearly, the zoomed images of a region of interest (ROI) from the corresponding images of Figure 6 are shown in Figure 7. Clearly, the proposed method is superior to the other methods in image quality.  
To quantitatively evaluate the proposed method for head phantom, all slices of reconstructed images were compared by RMSE, CC, and MSSIM, as shown in Table 3. Clearly, the proposed method provides the highest CC and MSSIM mean values and the lowest RMSE mean values. All the standard deviations of the proposed method are much lower than the other three methods. The results indicate that the proposed method has a better performance on motion artifact reduction.