# 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

Table 6: Comparison between different learning and optimization methods. The best scores are displayed in bold. PCC, Pearson correlation coefficient. Table 7 presents a comparison of the performance of the variant architectures for the discriminator previously displayed in Figure 3. Models A, B, and C had a different number of convolution layers in the input and output stages, and more than one convolution layer in the shared stage. In contrast, Models D, E, and F had only one convolution layer in the shared stage with a different number of convolution layers in the input and output stages. For the two different data flows, an independent discriminator design was employed in Model G. From the experimental results, three significant observations are worth noting. First, the independent discriminator architecture (Model G) exhibited higher performance than Models D, E, and F, due to the high discriminatory capability of the independent network. Second, Models A, B, and C outperformed the other models. This is because the deep weight-sharing constraint in the shared stage can learn the joint distribution of the aligned and unaligned data. Finally, Model C, which consists of two convolutions in the shared stage and two layers in the output stage, exhibited the most effective discriminatory capability, outperforming all other models in all metrics except for SSIM. As demonstrated in [48; 49], synthesizing an image by minimizing the perceptual loss for the early layers of the pretrained network tends to focus on low-level information, such as intensity, texture, and shape. Perceptual loss is helpful when there is misalignment in the training and test datasets. Layer selection for perceptual loss is a task-oriented problem. We considered five ReLU layers before max-pooling in the pretrained VGG16 network as in [48; 49]. The performance of the different perceptual layers is summarized in Table 8. The five layers were ReLUs 1_2, 2_2, 3_3, 4_3, and 5_3, with the high-layer ReLUs always including the early layer ones. Table 8 indicates that perceptual loss defined by high layers produced more accurate output than did the early layers. We also observed that the perceptual loss from ReLU {1_2,2_2,3_3,4_3} and ReLU {1_2,2_2,3_3,4_3,5_3} had minor quantitative differences. Our objective function contained six independent loss terms. The experiments reported above used all of the loss terms. To investigate the strength of each loss term, we employed ablation analysis to determine how performance was affected by each loss term. We trained each network with a different objective function five times using different initialization weights and report the average of the five trials for each objective function. The evaluation results are shown in Table 9. Beginning with adversarial loss alone, each loss term was added one by one. In this process, five metrics were used to analyze the change in performance, and relative MAE improvement was also calculated. We considered \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Discriminator** & **MAE** & **RMSE** & **PSNR** & **SSIM** & **PCC** \\ \hline Model A & 29.096 & 39.826 & 64.460 & 0.244 & 0.447 \\ Model B & 29.024 & 39.791 & 64.472 & **0.249** & 0.447 \\ Model C & **28.819** & **39.418** & **64.553** & 0.248 & **0.453** \\ Model D & 31.320 & 42.345 & 63.933 & 0.228 & 0.410 \\ Model E & 32.415 & 43.440 & 63.722 & 0.234 & 0.437 \\ Model F & 31.232 & 42.353 & 64.937 & 0.226 & 0.402 \\ Model G & 31.011 & 41.980 & 63.931 & 0.221 & 0.414 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Analysis of the discriminator architecture. The best scores are displayed in bold.