# Limited-Angle Computer Tomography with Truncated Projection Artifacts Removal
## 3 Results  
### Simulated Data  
To observe the effectiveness of artifact removal, our research uses SART to reconstruct the original data and the completed data separately. At the same time, to demonstrate the effectiveness of our algorithm, a diffusion-based TPA elimination method is used as a comparison which uses the low-frequency information in the updated area to compensate for the un-updated area [16]. MATLAB code is used to create a three-dimensional matrix to simulate the breast image and simulate the attenuation of X-ray irradiation through the breast to create projection data. The corresponding reconstruction process is also carried out on MATLAB R2017a. In our simulation data, tumors, ligaments and other objects are included in the artifact area. We use an ellipsoid with voxel value of 0.6 to simulate the breast, curves with voxel value of 0.8 to simulate the ligaments, and spheres with voxel value of 1 to simulate the tumor. The number of iterations of SART is 5 and the relaxation coefficient \(\lambda\) in Equation (1) is set to 0.1.  
The compressed thickness of the simulated breast was 60 mm and the selected section height is 50 mm on the \(Z\)-axis. In simulated data, the ligament was designed as a complex curve, which is helpful for us to observe the details when comparing the results with the original ones. The tumors in simulation data are spherical, which allows us to observe whether the edges of the tumor are distorted. In our study, different pixel values were designed for different tissues in the breast, representing their different X-ray absorptivity.  
Figure 7 shows the results of the simulation data experiments. By comparing the images reconstructed by different TPA-removed methods in Figure 7c,d with the SART reconstructed image in Figure 7b, it can be seen that both algorithms are effective in reducing TPA. Artifact areas on the left and right sides of the breast are magnified for observation on the right of Figure 7a-d. By comparing with the real image in Figure 7a, it can be found that the image reconstructed by our algorithm in Figure 7d can better remove the influence of TPA on reconstructed image and restore breast tissue obscured by the artifacts, while the image reconstructed by the diffusion method in Figure 7c still contains some residual artifacts. After the image comparison, we completed data analysis on the experimental results. The position of the comparison line is marked with a dashed line in Figure 7a and the profiles are shown in Figure 7e,f. By comparing the pixel values reconstructed by different methods in Figure 7e, it can be found that the pixel values reconstructed by our algorithm at the left end of the selected line (around 40 mm) and the right end of the selected line (around 200 mm) is most similar to the real values. To demonstrate the effectiveness of our algorithm, we computed gradient information of the box region in Figure 7e. As shown in Figure 7f, since the real value has not changed, its gradient is zero. Among the data reconstructed by different algorithms, the gradient of the data reconstructed by our algorithm is the smallest in the artifact area. Since a sharp change in gradients should not appear in normal tissue, thus the smoothing of gradients in the image in Figure 7f also illustrates that our algorithm can reduce artifacts better and improve image quality.