## 1 Introduction  
Recently, the speed, accuracy, and convenience of identifying the type and location of a disease have improved using diagnostic imaging modalities such as magnetic resonance imaging (MRI), positron emission tomography (PET), single photon emission computed tomography (SPECT), and computed tomography (CT), which is the most commonly used modality [1; 2].  
However, noise is inevitably caused by scattering rays, quantum noise, and detectors, as the images for medical diagnosis are displayed as digitized images through the conversion process of each device. Such noise that degrades the diagnostic accuracy is fatal for patients. In particular, noise is commonly observed under low-dose examinations and thoracic CT images are usually obtained under low-dose examinations to obtain improved contrast [3; 4].  
In the case of lung cancer, which is the most common cause of cancer death, various studies have demonstrated the feasibility of applying low-dose examinations for early diagnosis of lung cancer. A study by the National Lung Screening Trial Research Team showed the usefulness of low-dose CT [5]. In addition, the use of low-dose examinations is on the rise with the increase in awareness of the risk of ionizing radiation [6]. However, noise is inevitably generated due to the use of low-dose examinations [7; 8; 9].  
The reduction of noise as much as possible is necessary to avoid misdiagnosis by doctors. Therefore, to reduce noise, denoising filters such as Gaussian, median, and Wiener filters have been developed. In a Gaussian filter, after setting up the rotating symmetrical mask, the central pixel is calculated by increasing the weight as the standard deviation of the Gaussian distribution increases [10]. A median filter replaces its median masks with the median values of the surrounding pixels. The Wiener filter reduces noise by separating the image signal from the noise in the frequency domain. However, conventional denoising filters are applied equally to the entire image. Therefore, these are inefficient in filtering nonlinear noise and cause signal distortion. In particular, the image sharpness decreases due to the blurring effect, which is caused by an excessive thinning of the outline [11].  
To solve the above-mentioned problems, the non-local means (NLM) denoising algorithm was developed. The NLM denoising algorithm equalizes the interior pixel values while maintaining the outline by setting regions of interest (ROIs) and calculating the weight based on the intensities of the adjacent pixels and Euclidean distance. Therefore, the NLM denoising algorithm can offset the blurring effect [12]. [PERSON] et al. specifically applied the NLM denoising algorithm to MRI. They showed that the NLM algorithm preserved nearly 100% of the edge information in the image, while achieving the best signal-to-noise ratio (SNR) as compared with conventional denoising algorithms. Although they suggestedthe use of the NLM denoising algorithm in the clinical field on the basis of their research, there are time constraints due to the computational complexity [13]. To address this problem, we developed the fast non-local means (FNLM) denoising algorithm, which reduced the computational complexity by changing the weight calculations of the NLM denoising algorithm from two dimensions to one dimension. This technique can improve the time resolution of the NLM denoising algorithm [14; 15; 16; 17; 18].  
In particular, this study was performed in both simulation study and practical study using a male adult mesh (MASH) phantom and a five-year-old phantom. Therefore, the radiation exposure was prevented and more practical results were derived by applying FNLM denoising algorithm to actual CT image.  
Here, we demonstrated the feasibility of the FNLM denoising algorithm for noise reduction from thoracic CT images.