# Two-View Mammogram Synthesis from Single-View Data Using Generative Adversarial Networks
## 4 Discussion  
In this study, we compared the performance of CR-GAN with that of our proposed methods for CC-view synthesis from MLO views. Our results revealed the disadvantages of the method using only CR-GAN, in terms of the synthesized image quality. We also found that training using only CR-GAN takes quite a long time as the synthesized image resolution increases. Subsequently, we incorporated the PG technique into CR-GAN, and confirmed that it brings significant benefits in reducing the training time, except for the case of 128\(\times\)128 resolution. Additionally, the synthesized CC views came closer to the real views and the artifacts were less obvious with the adaptation of \(L_{FM}\), as can be seen from Figures 6 and 7, and the similarity metrics also increased the most in Table 3. Overall, our proposed method using both the PG technique and \(L_{FM}\) offers the best performance, in terms of the image quality and training time, for high-resolution CC-view synthesis. Although the unidirectional training time may be substantially shorter, the image quality is inferior to that of bi-directional training. Even with the approach utilizing the PG technique and \(L_{FM}\), synthesis failed in some cases, as shown in Figures 11-13. As such, complete representation--from which the name of CR-GAN is derived--has not been accomplished here. Notably, image synthesis was barely successful in cases of calcification. Nonetheless, the proposed method with the PG technique and \(L_{FM}\) at 512 \(\times\) 512 resolution provides a perspective on the calcification, as implied by the white specks in Figure 14. There is a limitation that the image quality was assessed by radiological technologists in this work. In fact, the diagnostic potential needs to be evaluated by radiologists or breast surgeons. We consider the insufficient volume of training data and the restricted batch sizes as reasonable causes of synthesis failure. In Figure 15, it can also be seen that the artifacts were more noticeable and the image quality was degraded with lower batch size. According to [48], [PERSON] et al. have successfully generated multi-view face images using labeled images of at least 200 subjects from Multi-PIE and 72,000 unlabeled images from CelebA [49] by CR-GAN with a batch size of 64. The number and variation of our used training data, consisting of images from approximately 3000 subjects, would surely have been too small to cover the whole latent space. [PERSON] et al. [26] have synthesized realistic high-resolution mammograms at 1280 \(\times\) 1240 resolution by PG-GAN using eight GPUs each with 16 GB memory. Although their used batch size was not specified, it is expected that they used batch sizes higher than 4, which was the available maximum batch size for the 512 \(\times\) 512 image syntheses in our training environment using only one 16 GB GPU. In fact, the models without \(L_{FM}\) using a batch size of 4 failed to synthesize 256 \(\times\) 256 images, due to the divergence of discriminator and generator losses. This suggests that such a small batch size could cause instability in the training. Subsequently, synthesis of 512 \(\times\) 512 images also resulted in failure, due to the same issue with the loss functions. We speculate that the small batch size makes the training unstable, potentially leading to the vanishing gradient problem. Taken together, we can expect improvements in the image quality if the training is performed with a larger image data set within a more powerful GPU environment. A powerful GPU would make it possible to apply larger batch sizes, and three or more vectors should be utilized in the \(L_{FM}\) calculation for stronger constraints on middle-layer representations. It would also be feasible to synthesize images at resolutions higher than 512 \(\times\) 512, which is essential for clinical mammograms. In addition, we did not conduct any validation to adjust the hyperparameters.