# DC2 Anet: Generating Lumbar Spine MR Images from CT Scan Data Based on Semi-Supervised Learning
## 3 Method
### Dual Cycle-Consistent Adversarial Network  
A GAN [25] is a generative model that is designed to generate synthetic samples directly from the desired data distribution without the need to model the underlying probability density function explicitly. It consists of two different networks that are trained simultaneously, with the generator network focused on image generation and the discriminator network used to distinguish between real samples and the synthetic images. The idea of using a cycle-consistent approach to regularize structural data has a long history in visual tracking [53] and structure from motion [54]. The cycle-consistent structure employed in the GAN (cycleGAN) [44] enables unsupervised learning, stitching two generator networks together head to toe so that the synthetic images can be translated into a forward cycle. In addition to the forward cycle, the cycleGAN also has a backward cycle to stabilize the training process and prevent mode collapse. The forward cycle enforces the translation from the CT domain to the MR domain, while the backward cycle moves from the MR domain to the CT domain.  
The proposed DC\({}^{2}\)Anet also applies a cycle-consistent structure for its unsupervised learning setup. However, the proposed network has a dual cycle-consistent structure for the adoption of semi-supervised learning: one cycle-consistent structure for supervised learning with aligned data and the other for unsupervised learning with unaligned data. A diagram of DC\({}^{2}\)Anet is presented in Figure 2. Because the forward and backward cycle-consistent networks with aligned data or unaligned data are similar, we only illustrate a forward cycle-consistent adversarial network with unaligned learning in Figure 2a and a backward cycle-consistent with aligned learning in Figure 2b.  
In the forward cycle-consistent adversarial network with unaligned learning, the \(Syn_{MR}\) network generates a synthetic MR image from a CT image, and this MR image is then used by the \(Syn_{CT}\) network to generate the original CT image in order to learn the domain structures. The input to the MR discriminator network is either a sample MR image from the real MR data or a synthetic MR image. The objective function for unaligned learning includes both cycle-consistent and adversarial loss. In the backward cycle-consistent adversarial network with aligned learning, a synthetic CT image is generated from an MR image, and this CT image is employed by the \(Syn_{MR}\) network to generate the original MR image. The CT discriminator is used to distinguish between the synthetic CT and reference CT images. In aligned learning, a reference image is matched with the synthetic image to restrain the generated structure of the output. Based on the cycle-consistent and adversarial loss, the objective function of aligned learning also considers, due to the use of the reference image, voxel-wise, gradient difference, structural, and perceptual loss within the pretrained VGG16 network [24]. The four switches are simultaneously employed to control the data flow from the reference image, and these are connected in aligned learning, but disconnected in unaligned learning. It is also important to note that the \(Syn_{MR}\) and \(Syn_{CT}\) networks utilized in the forward and backward cycles share the same weights.  
Figure 1: Illustration of the conversion of supervised learning to semi-supervised learning.