# DC2 Anet: Generating Lumbar Spine MR Images from CT Scan Data Based on Semi-Supervised Learning
## 3 Method
### Optimization of DC\({}^{2}\)Anet with Semi-Supervised Learning
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Perceptual Layers** & **MAE** & **RMSE** & **PSNR** & **SSIM** & **PCC** \\ \hline ReLU {1_2} & 29.147 & 39.858 & 64.459 & 0.241 & 0.442 \\ ReLU {1_2,2_2} & 29.058 & 39.787 & 64.477 & 0.243 & 0.449 \\ ReLU {1_2,2_2,3_3} & 28.882 & 39.596 & 64.530 & 0.245 & 0.446 \\ ReLU {1_2,2_2,3_3,4_3} & 28.825 & **39.383** & **64.574** & 0.241 & 0.448 \\ ReLU {1_2,2_2,3_3,4_3,5_3} & **28.819** & 39.418 & 64.553 & **0.248** & **0.453** \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Evaluation of variation in perceptual layers. The best scores are displayed in bold. adversarial loss alone to represent 0%, and the inclusion of all loss terms (the final row) was considered to be 100% when calculating relative MAE improvement. The synthesis results for the ablation analysis are presented in Figure 5. The performance of DC2 Anet generally improved with the addition of each loss term, with voxel-wise loss the most useful in terms of relative improvement. This is because voxel-wise loss and MAE are consistent with a per-pixel mean-error-based measure. Dual cycle-consistent and gradient difference loss exhibited relative improvement of 12.19% and 6.95%, respectively, while perceptual loss and structural similarity loss had a limited effect on the improvement of performance compared to the other forms of loss. However, when all terms were used, the occurrence of unnatural features in the synthetic MR images was significantly reduced. As a result of the above results, in the remainder of the experiments, we employed DC2 Anet with the following characteristics: alternating optimization of semi-supervised learning, Model C for the discriminator architecture



### Comparison with Baselines

To compare synthetic MR images produced using different methods quantitatively, we present box plots in Figure 6 representing the MAE, RMSE, PSRN, SSIM, and PCCs resulting from the use of multi-channel GAN [33], deep MR-to-CT [41], DiscoGAN [44], MR-GAN [45], and our proposed method. The circles next to the box plots represent a single image slice from the test dataset. The top and bottom box limits were calculated from \(Q25\) and \(Q75\), respectively. The green triangles and the horizontal lines denote the average and the median. The range of the box plot whiskers is given by \(\big{[}Q25-1.5\times(Q75-Q25),Q75+1.5\times(Q75-Q25)\big{]}\). Any data point that falls outside of this range is typically considered an outlier and indicated by a red cross. The averages and standard deviations displayed in Table 10 indicate that our proposed method outperformed the other methods for all measures, with the lowest MAE and RMSE and the highest PSNR, SSIM, and PCC, thus further verifying the utility of our architecture. In addition, \(t\)-tests were conducted on the results in Table 10, finding that agreement with the reference MR images was significantly lower \((p<0.05)\) for images obtained using the MR-GAN method than for the images obtained using the DC\({}^{2}\)Anet model. Figure 6: A comparison of the proposed approach with baseline methods based on (**a**) MAE, (**b**) RMSE, (**c**) PSNR, (**d**) SSIM, and (**e**) PCC metrics. The MAE and standard deviation for the first 20 of the 92 subjects are plotted in Figure 7, comparing DC\({}^{2}\)Anet with multi-channel GAN [33], deep MR-to-CT [41], DiscoGAN [44], and MR-GAN [45]. It can be seen that DC\({}^{2}\)Anet generated a smaller MAE than the other approaches for most of the subjects. However, for some subjects, the MR-GAN [45] approach produced smaller MAE than did DC\({}^{2}\)Anet, though the MR-GAN [45] was unstable for some subjects, such as Subject 04 and Subject 08. Figure 8 presents three examples of synthetic images produced by the proposed DC\({}^{2}\)Anet method, alongside the corresponding CT and MR images. The results for multi-channel GAN [33], deep MR-to-CT [41], DiscoGAN [44], and MR-GAN [45] are also presented for comparison purposes.