# Two-View Mammogram Synthesis from Single-View Data Using Generative Adversarial Networks
## 3 Results  
### Comparison of the Similarity Metrics by Training Methods  
The similarity metrics were calculated and compared between the real and synthesized CC-view mammograms for the test data set. Table 3 lists the averaged metrics and the required training time, with respect to the training settings. The highest metrics in each image resolution setting are in bold. We attempted to synthesize 256 \(\times\) 256 images with the method using only CR-GAN or the model incorporating the PG technique with batch of 4 in the bi-directional training. However, blank images with all pixel values set to a constant were generated, due to the discriminator losses in Equations (1) and (4) and the generator losses in Equations (2) and (5) diverging. Moreover, we also attempted to synthesize 512 \(\times\) 512 images using bi-directional training with the PG technique and the unidirectional training with both the PG technique and \(L_{FM}\). Nevertheless, these two methods also failed due to divergence of the loss functions. These results are listed as NA (not available) in Table 3. In addition, training using only CR-GAN for 512 \(\times\) 512 image syntheses took longer than a week, so we did not conduct training, in order to prevent the GPU from being subjected to such a long-term and high-heat load. Consequently, we investigated only bi-directional training with both the PG technique and \(L_{FM}\) as the only feasible method of those for synthesizing 512 \(\times\) 512 images. When synthesizing 128 \(\times\) 128 images through bi-directional training, there was a slight increase in the three similarity metrics (PSNR, MS-SSIM, and Cos_sim; \(p\) < 0.05) for the model incorporating the PG technique, compared with the method using only CR-GAN, as shown in Table 3. However, the method with PG required 21.8 h of training time; longer than the 16.8 h when using only CR-GAN. Next, there were statistically significant increases in all evaluated similarity metrics (\(p\) < 0.05) when using the model incorporating both the PG technique and \(L_{FM}\), compared with the model using only CR-GAN, although the training time was further extended. In the case of 256 \(\times\) 256 image synthesis, the model incorporating the PG technique notably reduces the training time to 36.4 h, compared with 87.9 h for the model using only CR-GAN. With regard to the similarity metrics, significant increases (\(p\) < 0.05) in SSIM, MS-SSIM, and Cos_sim are obtained with the method incorporating PG technique, compared to the method using only CR-GAN. When \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Resolution Batch Size** & **Model** & **Training Direction** & **PSNR** & **SSIM** & **MS-SSIM** & **Cos\_sim** & **Time (h)** \\ \hline \multirow{4}{*}{128 \(\times\) 128} & \multirow{2}{*}{20} & CR-GAN & 21.9 & 0.746 & 0.842 & 0.817 & 16.8 \\  & CR-GAN+PG & Bi-directional & 23.0 & 0.742 & 0.858 & 0.877 & 21.8 \\  & CR-GAN+PG+\(L_{FM}\) & & **23.9** & **0.754** & **0.883** & **0.889** & 23.0 \\ \cline{2-8}  & \multirow{4}{*}{10} & CR-GAN & 21.3 & 0.727 & 0.812 & 0.845 & 87.9 \\  & & CR-GAN+PG & Bi-directional & 20.2 & 0.736 & 0.827 & 0.871 & 36.4 \\  & & CR-GAN+PG+\(L_{FM}\) & & **23.9** & **0.767** & **0.857** & **0.890** & 38.2 \\ \cline{2-8}
256 \(\times\) 256 & \multirow{2}{*}{4} & CR-GAN+PG+\(L_{FM}\) & Unidirectional & 21.2 & 0.730 & 0.821 & 0.799 & 30.1 \\ \cline{2-8}  & & CR-GAN & \multirow{2}{*}{Bi-directional} & \multirow{2}{*}{NA} & \multirow{2}{*}{NA} & \multirow{2}{*}{NA} & \multirow{2}{*}{NA} & \multirow{2}{*}{NA} \\  & & CR-GAN+PG & & 23.1 & 0.766 & 0.852 & 0.876 & 72.8 \\ \hline \multirow{4}{*}{512 \(\times\) 512} & \multirow{4}{*}{4} & CR-GAN+PG & \multirow{2}{*}{Bi-directional} & NA & NA & NA & NA \\  & CR-GAN+PG+\(L_{FM}\) & & **22.7** & **0.766** & **0.831** & **0.868** & 112.4 \\ \cline{1-1} \cline{2-8}  & & CR-GAN+PG+\(L_{FM}\) & Unidirectional & NA & NA & NA & NA & NA \\ \hline \hline \end{tabular}  
* Not available.  
\end{table}