## 2 Related Works  
Denoising is one of the essential preprocessing techniques in digital image processing. There are numerous studies on deep learning-based denoising methods for a variety of applications [29]. In particular, the denoising technique plays an important role in the medical imaging field, following the as low as reasonably achievable (ALARA) principle. Therefore, numerous studies on noise reduction in LDCT using conventional image processing techniques have been proposed to obtain good quality reconstructed images. The studies are categorized into three groups: noise reduction in the sinogram domain [3; 4; 5; 6], iterative reconstruction [7; 8; 9; 10; 11; 12; 13], and noise reduction in the image domain [14; 15; 16; 17; 18; 19].  
The first group of noise reduction in LDCT is noise reduction in the sinogram domain. The key to noise reduction in the sinogram domain is filtering the noise before reconstruction. Nonlinear smoothing [3; 4], bilateral filtering [5], and other statistical approaches [6] are employed for noise reduction in the sinogram domain. These methods are convenient and efficient for removing artifacts (e.g., streak artifacts). However, these methods have problems, such as a removed microstructure or blurred edges.  
The second group of noise reduction in LDCT is iterative reconstruction methods. Numerous researchers have used iterative reconstruction methods for noise reduction. These methods iteratively optimize the objective function, which is defined by the tomographic system. Additionally, an iterative reconstruction method combined with a smoothing method has been proposed. Specifically, total variation [10; 11], nonlocal mean filtering [11; 12], dictionary learning [13], and other methods are used to improve the quality of the reconstructed image. Iterative reconstruction methods are very promising for noise reduction in LDCT, but these methods are time-consuming and hardware-intensive because of the high computational complexity. Thus, these methods are not commonly used in clinical practice.  
The last group of noise reduction in LDCT is noise reduction in the image domain. The key to noise reduction in the image domain is filtering the noise after reconstruction. Total variation [14] as well as block matching and 3D filtering [15; 16] are employed to reduce noise in LDCT. These methods reduce the noise efficiently but have problems, such as a removed microstructure or blurred edges, as the noise reduction in the sinogram indicated.  
As an extension of these methods, methods based on deep neural networks have been proposed. The most common methods of noise reduction using deep learning are training a network with paired LDCT and normal-dose CT (NDCT) images [17; 18; 19]. The residual encoder-decoder convolutional neural network [17], wavelet residual network [18], generative adversarial network (GAN) [19], and other various network architectures are employed to reduce noise in LDCT. These methods have exhibited superior performance in reducing noise in LDCT. However, the problem with these methods is that they require numerous paired LDCT and NDCT images. Multiple scans are required to obtain well-paired LDCT and NDCT images. Multiple human body scans require additional radiation exposure. Therefore, it is almost impossible to obtain numerous well-paired LDCT and NDCT images because of public health care issues.  
As research on the GAN actively progresses, methods [20; 21; 22] using a neural network trained on unpaired images have been proposed to solve the problem. These methods learn the distribution of NDCT images to reduce the noise in LDCT images. However, although the network is trained on unpaired LDCT and NDCT images, obtaining many LDCT and NDCT images is an expensive and sometimes unavailable option. For these reasons, we propose a deep learning-based method that can train a denoising neural network on only LDCT images.