# 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
[48], who produced impressive results in real-time style transfer and single-image super-resolution. The network contained two stride-one convolutions at the beginning and the end, two stride-two convolutions, nine residual blocks [46; 47], and two fractionally-strided convolutions with a stride of 0.5. Each residual block included two convolutions with 256 filters of a size of \(3\times 3\) and a stride of one. Instance normalization [56] and a rectified linear unit (ReLU) [57] activation function followed each convolution except in the final convolutional layer. The hyperbolic tangent (Tanh) activation function followed the final convolution to guarantee that the output was within \([-1,1]\). A detailed description of the synthesis network is presented in Table 4.

For the discriminator networks \(Dis_{MR}\) and \(Dis_{CT}\), we used a patch-based GAN (PatchGAN) [36] architecture, which aims to classify small overlapping image patches as either real or synthetic, rather than whole images. This patch-level discriminator architecture has fewer parameters than a whole-image discriminator and can emphasize detailed information in local areas. DC\({}^{2}\)Anet with semi-supervised learning has two different input flows, aligned and unaligned, with different shapes for the input data. The flow size of a volume of aligned data is \((N,H,W,2)\). \(N\) is the batch size; \(H\) and \(W\) are the image height and width, respectively; and 2 represents a concatenation of the synthetic and input images. The flow size of a volume of unaligned data is \((N,H,W,1)\), in which only a synthetic image can be used as input (indicated as 1). Therefore, a hybrid discriminator model was designed that consisted of two input stages, a shared stage, and two output stages. To balance the capability between synthesis and discriminator networks, the discriminator network was designed to be much \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Layer Name/Type** & **Output Size** & **Filter Size/Stride** & \
\begin{tabular}{c} **Number of** \\ **Conv. Layers** \\ \end{tabular} &
\begin{tabular}{c} **Number of** \\ **Parameters** \\ \end{tabular} \\ \hline Input image & \(H\times W\times 1\) & None & 0 & 0 \\ \hline Conv 1, IN & \(H\times W\times 64\) & \(7\times 7/1\) & 1 & 3200 \\ \hline Conv 2, IN & \(H/2\times W/2\times 128\) & \(3\times 3/2\) & 1 & 73,856 \\ \hline Conv 3, IN & \(H/4\times W/4\times 256\) & \(3\times 3/2\) & 1 & 295,168 \\ \hline Residual Block 1, IN & \(H/4\times W/4\times 256\) & \(3\times 3/2\) & 2 & 590,080 \\ \hline Residual Block 2, IN & \(H/4\times W/4\times 256\) & \(3\times 3/2\) & 2 & 590,080 \\ \hline Residual Block 3, IN & \(H/4\times W/4\times 256\) & \(3\times 3/2\) & 2 & 590,080 \\ \hline Residual Block 4, IN & \(H/4\times W/4\times 256\) & \(3\times 3/2\) & 2 & 590,080 \\ \hline Residual Block 5, IN & \(H/4\times W/4\times 256\) & \(3\times 3/2\) & 2 & 590,080 \\ \hline Residual Block 6, IN & \(H/4\times W/4\times 256\) & \(3\times 3/2\) & 2 & 590,080 \\ \hline Residual Block 7, IN & \(H/4\times W/4\times 256\) & \(3\times 3/2\) & 2 & 590,080 \\ \hline Residual Block 8, IN & \(H/4\times W/4\times 256\) & \(3\times 3/2\) & 2 & 590,080 \\ \hline Residual Block 9, IN & \(H/4\times W/4\times 256\) & \(3\times 3/2\) & 2 & 590,080 \\ \hline Fractional Conv 1, IN & \(H/2\times W/2\times 128\) & \(3\times 3/0.5\) & 1 & 295,040 \\ \hline Fractional Conv 2, IN & \(H\times W\times 64\) & \(3\times 3/0.5\) & 1 & 73,782 \\ \hline Conv 4, Tanh & \(H\times W\times 1\) & \(7\times 7/1\) & 1 & 3137 \\ \hline Total number of parameters & & & 6,054,913 \\ \hline Total number of parameters if instance normalization is applied & & 6,065,217 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Model architecture of the synthesis network. Layers marked with IN indicate that the convolution layer is followed by the instance normalization layer. The ReLU activation layers are omitted. shallower than the synthesis network because generating images is much more difficult than merely distinguishing real from synthetic images.