## 3 Results
### Numbers of the Focal Spots  
Figures 10 and 11 show the s-IGDT images acquired by using various numbers of focal spots and the differential images between the reference and obtained s-IGDT images, respectively. Despite an increase in the focal spots, the truncation artifacts still remained in the s-IGDT image obtained with the truncated projections and 41 focal spots. Also, the voxel value discrepancies were observed in the truncated regions of the s-IGDT image acquired with the truncated projections and 81 focal spots. Similar to the results for the s-IGDT images with the various lengths of the source array, the proposed method substantially alleviated the truncation artifacts in comparison to the PDC method, regardless of the variation in the number of focal spots. The voxel value distortion for the truncated regions was also restored by the proposed out-painting method.  
Figure 8: Voxel value profiles of the s-IGDT images obtained with the 660 mm X-ray source array.  
Figure 7: Differential images between the reference images and the s-IGDT images. (**a–c**), (**d–f**) and (**g–i**) correspond to Figure 6b–d, _f–h_ and j–l, respectively.  
Figures 12 and 13 present the voxel value profiles and the quantitative results for the s-IGDT images acquired with various numbers of focal spots, respectively. As observed in Figure 12, the proposed method restored the voxel values for the truncated and non-truncated regions in the s-IGDT image obtained with 81 focal spots. For the s-IGDT images obtained with various numbers of focal spots, the SNRs of the PDC and proposed methods were, on average, 19.62 and 76.25% higher than those of the s-IGDT images using the truncated projections, respectively. The degrees of the SNR improvements by the proposed method were 44.66-52.02% larger than those by the PDC method for the s-IGDT images  
Figure 10: Reconstructed s-IGDT images with (**a–d**) 21, (**e–h**) 41, and (**i–l**) 81 focal spots. The first to second columns represent the images reconstructed with the GT (reference) and truncated projections, respectively. The third to fourth columns correspond to the restored images using the PDC and proposed methods, respectively. The voxel value profiles were plotted along the yellow line.  
Figure 9: (**a**) SNRs, (**b**) NRMSEs, (**c**) PSNRs, and (**d**) SSIMs with error bars of the s-IGDT images with the different lengths of the linear X-ray source array, respectively.  
obtained with various numbers of focal spots. Comparing the conventional s-IGDT imaging and PDC methods, the proposed method decreased the NRMSEs of the s-IGDT images by 57.35-58.60 and 29.83-30.23%, respectively. Across all the numbers of the focal spots, the lowest NRMSEs were consistently observed with the proposed method. The proposed method increased the PSNRs of the s-IGDT images obtained with various numbers of focal spots by an average of 35.37 and 4.16% compared to the truncated s-IGDT images and PDC method, respectively. For all the numbers of the focal spots, the proposed method consistently yielded higher SSIMs than the truncated s-IGDT images with an average increase of 32.28%. The SSIMs of the PDC method were slightly higher than those of the proposed method for the s-IGDT images obtained with 41 and 81 focal spots.