# DC2 Anet: Generating Lumbar Spine MR Images from CT Scan Data Based on Semi-Supervised Learning
## 1 Introduction  
Computed tomography (CT) scanning is a medical imaging technique that is widely used for diagnostic and therapeutic purposes in a variety of clinical applications. Magnetic resonance imaging (MRI) is another imaging technique that visualizes anatomical details and is used in radiology and nuclear medicine. A comparison of the strengths and weaknesses of these imaging approaches is shown in Table 1. Unlike CT scans, MRI can detect slight differences in soft tissue, ligaments, and organs, which is beneficial for diagnosis. However, MRI is not only much more expensive, but also requires more time to produce its results, meaning that patients often prefer CT scans to MRI. Lumbar disc herniation is common among the elderly and people who sit for long periods. The use of MRI to observe the spinal cord and the disc signals of the lumbar spine is of great importance in the treatment of this condition. However, some patients with claustrophobia or cardiac pacemakers are prevented from receiving an MRI due to possible injury. Thus, the ability to generate a reliable magnetic resonance (MR) image from a CT scan for these patients is vital. This would not onlyincrease the diagnostic value of CT scans, but also provide additional reference information for diagnosis. Thus, in this study, we propose a synthesis method based on convolutional neural networks (CNNs) [1; 2] with adversarial training [3] to construct a lumbar spine MR image from CT scan data. In recent years, researchers have increasingly searched for ways to replace CT scans with MRI when planning for radiation therapy [4; 5; 6]. However, CT-based MR image construction has received little attention. It is challenging to generate an MR image directly from a CT image using a linear model because it is difficult to produce high-level image domains based on low-level ones. In response to this, we propose a synthesis method based on convolutional neural networks (CNNs) [1] with adversarial training [3] to produce a lumbar spine MR image from a CT scan. In this process, the development of an objective function for the deep neural network is essential [7; 8]. An objective function is a combination of loss terms that maps a real number that intuitively represents the \"cost\" associated with the performance of a predefined network at a certain status. The optimization process seeks to minimize this cost by updating trainable variables to determine an optimal network. Synthetic images in medical imaging need to not only be realistic, i.e., they cannot be distinguished from genuine images by human experts, but also be very similar to reference images. In this study, we propose a novel objective function that balances between two quantitative loss terms and three qualitative loss terms to construct lumbar spine MR images from CT images. A dual cycle-consistent loss is also included for semi-supervised learning that alternates between optimizing supervised and unsupervised learning in order to seek a global minimum for the optimal network. Experimental results based on quantitative and qualitative evaluations prove the superiority of the proposed method compared with other state-of-the-art methods. The main contributions of this study are as follows:  
* An objective function is proposed to balance quantitative and qualitative loss terms to construct a realistic and accurate synthetic MR image. This function consists of adversarial, dual cycle-consistent, voxel-wise, gradient difference, perceptual, and structural similarity losses. Using ablation analysis, the importance and effectiveness of each of these loss terms are investigated.