## 4 Discussion
The PSNR and CC values can differ from visual evaluation, as these factors are measured mathematically. However, as shown in Figures 3 and 6, the image that was the applied FNLM denoising algorithm visually showed the clearest image without any blurring. To prove the enhancement of noise level and sharpness, we measured the signal intensity of the images. Figures 8 and 9 show the signal intensity profiles of the images that are the applied Wiener filter and FNLM denoising algorithm, respectively. The Wiener filter, only, was analyzed to compare with the FNLM denoising algorithm because the Wiener filter showed the best performance in almost all of the evaluations among the conventional denoising filters. Figure 8 is the signal intensity profile of the image that was obtained from the MASH phantom. The spine region was utilized to obtain this profile. The boxes represent the noise level in the region that should represent smooth signal intensity. The gap of signal intensity between the highest and the lowest in box_a is larger than the gap of signal intensity in box_b. In other words, it means that box_a represented the mottled image and the circles represented the sharpness of the edge, circle_b showed the definite contrast as compared with circle_a, and moreover, the edge information on the opposite of circle_a was distorted. On the contrary, the profile in Figure 8 represents symmetrical result because the FNLM denoising algorithm considers the geometrical composition of the entire image by using the Euclidean distance. Figure 8: The (**a,b**) are signal intensity profiles of the MASH phantom images applied the Wiener filter and the FNLM denoising algorithm, respectively. The graphs represent the signal intensity of the yellow lines in the images. The boxes represent the denoising performance of the Wiener filter and the FNLM denoising algorithm. The circles represent the sharpness of the images. Figure 9 is the signal intensity profiles of the images that were obtained from the five-year-old phantom. The spine region was utilized similar to the image of the MASH phantom. The boxes also represent the noise level in the region that should represent smooth signal intensity. In the profile in Figure 9b, the signal intensity of box_b is almost flat and also the contrast of circle_b definitely show as compared with the profile in Figure 9a. Therefore, we confirmed that the FNLM denoising algorithm is more efficient than the conventional denoising filters for reducing the noise and improving sharpness by measuring the signal intensity of each image. In addition, the actual computational times were measured using a MATLAB program to compare the time resolution of the FNLM and NLM denoising algorithms. The actual operation time was measured and the average of 20 measurements was calculated. As a result, the average computational time of the FNLM denoising algorithm was 0.998 s, while that of the NLM denoising algorithm was 17.428 s. The time resolution of the FNLM denoising algorithm was approximately 17.5\(\times\) better than the conventional algorithm due to a simplified computation of its weights. Observing Equation (2), the X-axis (\(m\)) and Y-axis (\(n\)) components of the image are defined in this equation. In other words, the presence of two axes necessitates complicated computations along two dimensions. Therefore, as shown in Equation (5), the size of the matrix was reshaped from \((m,n)\) to \((m\times n,1)\) because the computer treats \((m\times n,1)\) as a one-dimensional vector, thus, simplifying the computational complexity [34, 35]. Figure 10 shows the time resolution of the FNLM and NLM algorithms. It can be observed that the proposed FNLM denoising algorithm significantly improved the time resolution as compared with the conventional NLM denoising algorithm.