# Two-View Mammogram Synthesis from Single-View Data Using Generative Adversarial Networks
## 2 Materials and Methods
### Training Networks
#### 2.1.1 CR-Gan
While the original CR-GAN synthesizes 128 \(\times\) 128 images, as can be determined from the code [34], we experimented with generating 256 \(\times\) 256 and 512 \(\times\) 512 images by adding convolution layers into the networks. Table 1 shows the architecture of \(G\) in the modified CR-GAN for 256 \(\times\) 256 image syntheses. The second through sixth middle layers consist of Upsample (2\(\times\) up-sampling by nearest neighbor method) and Conv2d (two-dimensional convolution; kernel size = 3, stride = 1, padding = 1). In each layer, the output feature vector from Conv2d after Upsample and that after passing repeatedly through batch normalization (BN), ReLU activation, Upsample, and Conv2d, in the order indicated by the right arrows (\(\rightarrow\)), are summed. In the sixth layer, BN and ReLU are adapted again. Finally, the seventh layer translates the feature vector to a 256 \(\times\) 256 image with 3 channels. Table 2 shows the architecture of \(D\). In the second through seventh layers, the feature vector after passing through Conv2d and AvgPool2d (two-dimensional average pooling; kernel size = 2), and that after passing through ReLU activation in addition to above the two functions repeatedly (in the order shown by the right arrows), are summed. In the eighth layer, the feature vector is fully connected, in order to output the estimated view information after proceeding with the Softmax function. In addition, the output from the seventh layer is translated to a scalar expressing the image quality, without the Softmax function. Batch normalization is not used in \(D\). \(E\) has a similar architecture to \(D\), but the eighth layer outputs the view information vector and image vector, with a shape of 256 \(\times\) 256 \(\times\) 3. As a side note, [PERSON] et al. have leveraged not only labeled images with view information, but also unlabeled images in self-supervised learning [32]. Meanwhile, the view information of mammograms is usually obvious, and this information can be easily extracted from the images. Therefore, we used only labeled mammograms without self-supervised learning. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Type** & **Description of Type** & **Norm 1** & **Activation** & **Input Shape 2** & **Output Shape 2** \\ \hline Input projection & FC 3  & Linear transformation & & & 256 & 4 \(\times\) 4 \(\times\) 512 \\ Layer 1 & & & & 4 \(\times\) 4 \(\times\) 512 & 8 \(\times\) 8 \(\times\) 512 \\ Layer 2 & & \{Upsample\(\rightarrow\)Conv2d(3,1,1)\} & – & – & 8 \(\times\) 8 \(\times\) 512 & 16 \(\times\) 16 \(\times\) 256 \\ Layer 3 & Convolution1 & +(BN\(\rightarrow\)ReLU\(\rightarrow\)Upsample & & & 16 \(\times\) 16 \(\times\) 256 & 32 \(\times\) 32 \(\times\) 128 \\ Layer 4 & & \(\rightarrow\)BN\(\rightarrow\)ReLU\(\rightarrow\)Conv2d(3,1,1)\} & & & 32 \(\times\) 32 \(\times\) 128 & 64 \(\times\) 64 \(\times\) 64 \\ Layer 5 & & & & 64 \(\times\) 64 \(\times\) 64 & 128 \(\times\) 128 \(\times\) 64 \\ Layer 6 & & & BN & ReLU & 128 \(\times\) 128 \(\times\) 64 & 256 \(\times\) 256 \(\times\) 64 \\ Layer 7 & Convolution2 & Conv2d(3,