# 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
The spinal cord region in the central area of the image, the most important element of the image, is enlarged to evaluate the reconstruction capability of each method. DC\({}^{2}\)Anet learned to differentiate between different structures with similar intensity values in CT images, but not in MR images, such as a vertebra, fat tissue, and disc signals. DC\({}^{2}\)Anet also preserved the continuity, smoothness, and semantics of the original images in the synthetic results because our objective function with semi-supervised learning led the synthetic MR images to be similar to the reference images. In CT-based MR image generation, the accurate reconstruction of the disc signal, the degree of disc protrusion, the degree of stenosis, and the the local sac are essential in the analysis of lumbar vertebra. We can see that the disc signal and the local sac in the synthetic MR image obtained using the proposed DC\({}^{2}\)Anet looked more similar to the reference MR image compared to the other methods. The structures of the muscle and fat tissue had a highest similarity. However, the proposed method exhibited limitations in the reconstruction of the degree of disc protrusion and the degree of stenosis. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Methods** & **MAE** & **RMSE** & **PSNR** & **SSIM** & **PCC** \\ \hline Multi-Channel & \multirow{2}{*}{\(29.245\pm 7.786\)} & \multirow{2}{*}{\(40.038\pm 8.913\)} & \multirow{2}{*}{\(64.428\pm 1.956\)} & \multirow{2}{*}{\(0.240\pm 0.066\)} & \multirow{2}{*}{\(0.447\pm 0.146\)} \\ GAN [33] & & & & & \\ Deep & \multirow{2}{*}{\(32.632\pm 8.239\)} & \multirow{2}{*}{\(44.320\pm 9.369\)} & \multirow{2}{*}{\(63.524\pm 1.855\)} & \multirow{2}{*}{\(0.219\pm 0.066\)} & \multirow{2}{*}{\(0.388\pm 0.160\)} \\ MR-to-CT [41] & & & & & \\ DiscoGAN & \multirow{2}{*}{\(33.863\pm 9.031\)} & \multirow{2}{*}{\(46.317\pm 9.853\)} & \multirow{2}{*}{\(63.130\pm 1.756\)} & \multirow{2}{*}{\(0.209\pm 0.061\)} & \multirow{2}{*}{\(0.334\pm 0.136\)} \\
[44] & & & & & \\ MR-GAN & \multirow{2}{*}{\(29.276\pm 7.218\)} & \multirow{2}{*}{\(39.989\pm 8.167\)} & \multirow{2}{*}{\(64.402\pm 1.769\)} & \multirow{2}{*}{\(0.237\pm 0.066\)} & \multirow{2}{*}{\(0.450\pm 0.144\)} \\
[45] & & & & & \\ DC\({}^{2}\)Anet & \multirow{2}{*}{\(\mathbf{28.819\pm 7.655\)}} & \multirow{2}{*}{\(\mathbf{39.418\pm 8.660\)}} & \multirow{2}{*}{\(\mathbf{64.553\pm 1.890\)}} & \multirow{2}{*}{\(\mathbf{0.248\pm 0.072\)}} & \multirow{2}{*}{\(\mathbf{0.453\pm 0.146\)}} \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Overall statistics for five measures of model quality: MAE, RMSE, PSNR, SSIM, and PCC. The average and standard deviation for each measure from 92 subjects in a lumbar vertebra dataset are presented for five methods. The best scores are displayed in bold. Figure 7: MAE computed for the first 20 of the 92 subjects in the test dataset. ## 5 Conclusions

In this work, we proposed an objective function and a general synthesis system, DC\({}^{2}\)Anet, that employs semi-supervised learning to generate lumbar spine MR images from single-sequence CT scans. Our objective function included six independent loss terms. Using ablation analysis, we assessed in detail the effectiveness and relative importance of each loss term. Performance was improved by adding each loss term because each had its own particular strengths and weaknesses. DC\({}^{2}\)Anet using semi-supervised learning can significantly outperform supervised and unsupervised learning approaches. To further improve the accuracy and to seek the global minimum of the objective function, alternating optimizing was much more efficient than the integrated optimization of DC\({}^{2}\)Anet. We applied our method to generate MR images from their corresponding CT images, demonstrating

Figure 8: Qualitative comparisons of DC\({}^{2}\)Anet and baseline methods. Rows 1, 3, and 5 show CT images, synthetic images, and the reference image. Rows 2, 4, and 6 show the enlarged spinal cord of the corresponding images.