## 3 Results and Discussion
### Evaluation Method of NLM Noise Reduction Algorithm in MR Imaging  
The methods for evaluating the effectiveness of the noise reduction algorithm can be divided into comparison evaluation and quantitative evaluation parameters. The comparison evaluation parameter analyzes the similarities and differences of two images, including: peak signal to noise ratio (PSNR), root mean square error (RMSE), and structural similarity (SSIM). The quantitative evaluation parameter is a method of numerically representing information about the noise included in each MR image, and is generally calculated with the image quality factor (signal or contrast): signal to noise ratio (SNR) and contrast to noise ratio (CNR). Figure 7 shows the overall summary for publication numbers with respect to the evaluation method. Table 5 describes the characteristics for the evaluation method of NLM noise reduction algorithm in MR imaging of the 25 included papers. Of the 25 papers identified, the comparison evaluation parameter category represented the largest number of studies (\(n=18\)) [39; 42; 43; 44; 46; 47; 48; 49; 51; 54; 55; 56; 57; 58; 60; 61; 62; 63], followed by the quantitative evaluation parameter category (\(n=4\)) [40; 41; 52; 59], and finally the category containing \"both\" parameters (\(n=3\)) [45; 50; 53]. Papers related to the application of the NLM noise reduction algorithm to MR images using the comparison evaluation parameter with RMSE were first published in 2008. Figure 7: (a) Graph of the number of publications using MR imaging with the NLM noise reduction algorithm for various evaluation parameters. The final classification included 25 papers; of those, three major categories of techniques were investigated. (b) The total number of papers as a function of the publication year. Among the comparison evaluation parameters, the most frequently published results were from studies using only PSNR (\(n=7\)). Additionally, eight papers were published as a result of evaluations using other factors along with the PSNR parameter. PSNR is a numerical representation of the power of the noise relative to the maximum power a signal can represent and is mainly used when evaluating the loss of an image, including the diagnostic field. In particular, the reason why it is so frequently used for noise evaluation in MR images is that PSNR is able to estimate the mean square error (MSE) value and the maximum signal value simultaneously, thereby confirming the overall noise distribution. PSNR is able to accurately measure the loss rate through the comparison of images, where the larger the value, the better the result. SSIM is used as a comparison evaluation parameter in the order of PSNR and is a factor that evaluates the similarity of the original image to the distortion of the image, where values closer to 1 represent better results. However, the results from only one study evaluating SSIM was used, and it was mostly measured with PSNR and RMSE evaluation factors (\(n=8\)) to confirm the effectiveness of the NLM noise reduction algorithm on MR images. Among the quantitative evaluation parameters, the most frequent results were from studies using only SNR (\(n=4\)). However, the evaluation ratio of SNR and CNR was almost the same, which means that there is no significant difference between the signal value and contrast value in the quantitative evaluation process.