# 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
Based on the related works presented in Table 2, the number of discriminator layers was fixed at five, and the variant architectures of the hybrid discriminator are presented in Figure 3.

Models A-F represent variations of the input, shared, and output stages. Model G is the independent discriminator for unaligned and aligned data flows. Each aligned data flow consisted of a \(300\times 200\) synthetic image and a corresponding \(300\times 200\) input domain image, and each unaligned data flow had only a \(300\times 200\) synthetic image as input to the discriminator. All convolutions in the discriminator conducted \(4\times 4\) filters with a stride of 2. A leaky rectified activation (LeakyReLU) [58] followed each of the convolutions as the activation function, except for the final convolution. ## 4 Experimental Results and Discussion

### Implementation Details

To stabilize the DC\({}^{2}\)Anet training process, we used an image pooling technique [59] that updates the discriminator networks \(Dis_{MR}\) and \(Dis_{CT}\) using a history of synthetic images rather than the ones generated by the latest synthesis networks. We maintained an image pool buffer that stored the 50 previously-synthesized images. We also conducted data augmentation using random horizontal flipping (\(-5\)-\(5\) degree rotation) and the random translation of up to 15 pixels in each spatial dimension in the training images. DC\({}^{2}\)Anet was trained with mini-batch stochastic gradient descent (SGD) [60] with a mini-batch size of one. All weights were initialized from a zero-centered truncated normal distribution with a standard deviation of 0.02. All networks were trained with a learning rate of 0.0002 for the first 100,000 iterations and a linearly decaying rate that went to zero over the next 100,000 iterations. Adam is one of the most pervasive and robust optimizers used in various field [61; 62]. The model was also optimized using the Adam optimizer [63] with \(\beta_{1}=0.5\) and \(\beta_{2}=0.999\), as suggested in [28]. For all experiments, the following empirical values were used to train the synthesis networks: \(\lambda_{cycle}=10\), \(\lambda_{oxel}=100\), \(\lambda_{grad}=100\), \(\lambda_{perc}=1\), and \(\lambda_{struc}=0.05\)

Figure 3: The variant architectures of the hybrid discriminator. Models A–F are hybrid discriminators for the aligned and unaligned data flow. Model G consists of two independent discriminators. In LeakyReLU, the slope of the leak was set to 0.2. Reflection padding was used to reduce artifacts instead of zero padding in the convolution layers. The model took about 48 h to train for 200,000 iterations using a single GeForce GTX 1080 Ti GPU. The code and pretrained models are available at [[https://github.com/ChengBinJin/SpineC2M](https://github.com/ChengBinJin/SpineC2M)]([https://github.com/ChengBinJin/SpineC2M](https://github.com/ChengBinJin/SpineC2M)). ### Data Acquisition

Our lumbar spine dataset consisted of 641 patients, each with CT and MR images. The CT image was acquired helically on a GE Revolution CT scanner with a tube voltage of 120 kV, an exposure of 450 mAs, and a slice thickness of 1.00 mm. The MR image for each patient was obtained using a Siemens 3.0T Trio TIM MR scanner with T2 3D (with a repetition time of 4320 ms, an echo time of 95 ms, and a flip angle of 150\({}^{\circ}\)). To allow the voxel-wise comparison of the synthetic and reference MR images, the CT image was manually aligned to the MR image to produce voxel-level correspondence. After alignment, the CT and MR images from the same patient had the same image size and spacing. Because only the lumbar spine region was considered, we cropped the aligned CT and MR images to reduce the computational burden, producing a final preprocessed image size of \(300\times 200\times 40\) (40-48 slices depending on the alignment quality) with the same voxel size (\(1.00\times 1.00\times 1.00\) mm). We randomly separated the 641 patients into two groups: 549 patients for the training set and 92 patients for the test set.