Optimization of Fast Non-Local Means Noise Reduction Algorithm Parameter in Computed Tomographic Phantom Images Using 3D Printing Technology

Noise in computed tomography (CT) is inevitably generated, which lowers the accuracy of disease diagnosis. The non-local means approach, a software technique for reducing noise, is widely used in medical imaging. In this study, we propose a noise reduction algorithm based on fast non-local means (FNLMs) and apply it to CT images of a phantom created using 3D printing technology. The self-produced phantom was manufactured using filaments with similar density to human brain tissues. To quantitatively evaluate image quality, the contrast-to-noise ratio (CNR), coefficient of variation (COV), and normalized noise power spectrum (NNPS) were calculated. The results demonstrate that the optimized smoothing factors of FNLMs are 0.08, 0.16, 0.22, 0.25, and 0.32 at 0.001, 0.005, 0.01, 0.05, and 0.1 of noise intensities, respectively. In addition, we compared the optimized FNLMs with noisy, local filters and total variation algorithms. As a result, FNLMs showed superior performance compared to various denoising techniques. Particularly, comparing the optimized FNLMs to the noisy images, the CNR improved by 6.53 to 16.34 times, COV improved by 6.55 to 18.28 times, and the NNPS improved by 10−2 mm2 on average. In conclusion, our approach shows significant potential in enhancing CT image quality with anthropomorphic phantoms, thus addressing the noise issue and improving diagnostic accuracy.


Introduction
In the field of medical imaging, computed tomography (CT) using X-rays has provided significant advantages as a non-invasive examination technique, offering patient information without the need for surgery [1,2].However, despite the various advantages of CT in providing patient information for diagnosis and patient management, there is a potential risk of radiation exposure [3].Low-dose CT has been introduced and implemented to reduce the radiation dose in patients.However, in the process of image acquisition, noise is inevitably generated, owing to hardware errors, patient-source-related errors, and electrical interference, which degrade the diagnostic accuracy of the acquired image [4][5][6][7][8].Particularly, low-dose CT scans exacerbate the noise issue, owing to an insufficient number of X-ray photons and increased influence of scattered rays [9][10][11][12][13].
To solve this issue, researchers have developed various noise reduction algorithms, such as the Gaussian filter, Wiener filter, and total-variation (TV) noise reduction algo-rithm, which are implemented using software-based image processing techniques [14,15].However, these algorithms have the disadvantage of destroying image details during the noise reduction process.Additionally, detailed features and high-frequency signals can be reduced in the filtered region, thereby reducing the image resolution and sharpness.These limitations are due to the algorithms reducing noise without considering the similarity to neighboring pixels [16,17].By contrast, the fast non-local means (FNLM) algorithm is a noise reduction algorithm that improves the speed of the non-local means (NLM) algorithm and uses a non-local means technique to reduce noise by considering the similarity to neighboring pixels [18,19].This enables the accurate preservation of the image details, thereby solving the issue of image degradation.Moreover, the FNLM algorithm employs an NLM technique to explore similar patterns across the entire image and shows a higher adaptation to diverse noise types.
In addition to noise and CT image processing, several other factors contribute to the degradation of image quality, including artifacts, and blurring effects arising from device deterioration or patient motion [20,21].To address these issues, the application of specific quality control (QC) measures is essential [22][23][24][25].In this case, QC includes optimal device setting estimation and image acquisition processes to ensure image accuracy.Particularly, the image accuracy was maintained through quantitative evaluations based on a devicespecific human phantom [26].These phantoms serve as standardized reference objects, allowing researchers to assess image quality, identify artifacts, and optimize device settings to enhance diagnostic accuracy [27,28].
Because 3D printing techniques are cost-effective and allow for flexible design changes, large numbers of anthropomorphic phantoms can be printed for a variety of environments and purposes.In addition, 3D printing technology has shown an exponential growth, and its applications in the medical field are increasing.Three-dimensional printing techniques offer efficient production of objects featuring intricate internal structures that are appropriate for CT and magnetic resonance imaging (MRI) applications [29,30].More recently, patient-specific surgical phantoms have been fabricated based on 3D printing technology to improve surgical planning and serve as visual aids to explain surgery to patients, assisting patients with surgical decisions.Moreover, the number of deaths caused by cardiovascular diseases is increasing rapidly in recent years, thus personalized 3D-printing phantoms are used to plan surgeries for patients with various types of cardiovascular diseases and to train clinicians to reduce procedure-related complications and improve patient care [31,32].Based on these advantages, 3D printing techniques have been applied in various medical processing studies, such as the evaluation of reconstruction algorithms by Solomon et al. [33].Therefore, the purpose of this study was to optimize the smoothing factor of the FNLM noise-reduction algorithm using CT images of a 3D-printed phantom.For this purpose, a phantom capable of simulating bone and brain tissues was fabricated using 3D printing to analyze the optimized smoothing factor of the FNLM noise reduction algorithm in specific anatomical structures.To quantitatively evaluate the performance of the FNLM noise reduction algorithm in CT images, local filtering techniques, such as the Gaussian filter, Wiener filter, and TV noise reduction algorithm, were compared with various noise intensity evaluation factors.

FNLM Noise Reduction Algorithm Modeling
The NLM noise reduction algorithm has demonstrated remarkable efficacy in noise reduction [34,35].Moreover, NLM effectively resolves issues commonly generated by local filtering techniques for noise reduction, such as signal distortion and blurring.This is because the NLM noise reduction algorithm compares the overall geometric composition using the Euclidean distance as a weight, as opposed to using a sliding technique on the entire image, as in the Gaussian and Wiener filters.The NLM noise reduction algorithm is defined as follows [36]: where the weight ω(m, n) is defined as where τ is the number of pixels; G σ (τ) is the Gaussian distribution with variance σ 2 of the number of background pixels; ||I(M + τ) − I(n + τ)|| 2  2 is the intensity difference between adjacent pixels based on the Euclidean distance value; and Z(m) is the leveling constant, defined as The FNLM algorithm modifies the calculation of ω(m, n) from two dimensions to one dimension.The modified ω(m, n) is defined as where τ is defined as n − m; s is defined as m + τ; and H i is defined as The FNLM noise reduction algorithm improves processing speed approximately 30 times in comparison with the NLM noise reduction algorithm [18].This enhancement is achieved by simplifying the process using one-dimensional computations.

CT Image Parameters
We used a 128-slice CT system (SOMATOM Definition AS+, Siemens Healthcare, Germany) to obtain the phantom CT images.The images of the self-produced phantom were acquired with the following parameters: 250 mAs, 120 kVp, a pitch of 0.55, a matrix size of 512 × 512, and a slice thickness of 5.0 mm.The acquired phantom images were processed using a standard algorithm.

3D Printing Technology and CT Phantom Image Acquisition
We used a 3D printer with a fused filament fabrication (FFF) technique (Ultimaker3 Extended, Ultimaker, Utrecht, the Netherlands) to produce a self-produced phantom that could imitate the human skull and brain tissues.The self-produced phantom case and blocks were produced using diverse filaments through the FFF technique of the 3D printer.Figure 1 shows the components of the 3D printer with the FFF technique.entire image, as in the Gaussian and Wiener filters.The NLM noise reduction algorithm is defined as follows [36]: where the weight ω(m, n) is defined as where τ is the number of pixels; G σ (τ) is the Gaussian distribution with variance σ 2 of the number of background pixels; ‖I(M + τ) − I(n + τ)‖ 2 2 is the intensity difference between adjacent pixels based on the Euclidean distance value; and Z(m) is the leveling constant, defined as The FNLM algorithm modifies the calculation of ω(m, n) from two dimensions to one dimension.The modified ω(m, n) is defined as where τ is defined as n − m; s is defined as m + τ; and H i is defined as The FNLM noise reduction algorithm improves processing speed approximately 30 times in comparison with the NLM noise reduction algorithm [18].This enhancement is achieved by simplifying the process using one-dimensional computations.

CT Image Parameters
We used a 128-slice CT system (SOMATOM Definition AS+, Siemens Healthcare, Germany) to obtain the phantom CT images.The images of the self-produced phantom were acquired with the following parameters: 250 mAs, 120 kVp, a pitch of 0.55, a matrix size of 512 × 512, and a slice thickness of 5.0 mm.The acquired phantom images were processed using a standard algorithm.

3D Printing Technology and CT Phantom Image Acquisition
We used a 3D printer with a fused filament fabrication (FFF) technique (Ultimaker3 Extended, Ultimaker, Utrecht, the Netherlands) to produce a self-produced phantom that could imitate the human skull and brain tissues.The self-produced phantom case and blocks were produced using diverse filaments through the FFF technique of the 3D printer.Figure 1 shows the components of the 3D printer with the FFF technique.Using SOLIDWORKS software (ver.2019; Dassault Systèmes, Waltham, MA, USA), we designed a self-produced phantom case with dimensions of 16 cm, closely resembling the average diameter of a human skull.The case interior was perforated with five insertion holes for the blocks.Converting this design data into the STL format ensured compatibility with the 3D printer.Subsequently, CURA software (Ultimaker, the Netherlands) was employed to generate the necessary G-code and configure the hardware and software settings of the 3D printer.The self-produced phantom was then fabricated using Polylactic Acid (PLA) filaments with a density similar to that of human tissue, following the G-code instructions.Figure 2 shows the blueprint and 3D printer output for the phantom case.Using SOLIDWORKS software (ver.2019; Dassault Systèmes, Waltham, MA, USA), we designed a self-produced phantom case with dimensions of 16 cm, closely resembling the average diameter of a human skull.The case interior was perforated with five insertion holes for the blocks.Converting this design data into the STL format ensured compatibility with the 3D printer.Subsequently, CURA software (Ultimaker, the Netherlands) was employed to generate the necessary G-code and configure the hardware and software settings of the 3D printer.The self-produced phantom was then fabricated using Polylactic Acid (PLA) filaments with a density similar to that of human tissue, following the G-code instructions.Figure 2 shows the blueprint and 3D printer output for the phantom case.Cylindrical blocks (6 and 2.5 cm in height and diameter, respectively) were designed to fit into the self-produced phantom case.These blocks were engineered to mimic the density of the human brain tissue (Table 1).For printing, we used acrylonitrile butadiene styrene (ABS), wood, and bronze filaments, including XT-CF20, a co-polyester-based carbon fiber composite material.We produced phantom blocks using a 3D printer, employing the same printing process as that used for the case.Figure 2 shows the blueprint and 3D printer outputs of the phantom blocks.We obtained the self-produced phantom CT images to assess the linear attenuation coefficient.As shown in Figure 3, the inserted materials were XT-CF20, wood, air, ABS, and bronze.To simulate CT images under low-dose conditions, noisy images were obtained by adding zero-centered Gaussian noise with intensities of 0.001, 0.005, 0.01, 0.05, and 0.1 using MATLAB software (ver.2023a; MathWorks, Boston, MA, USA).Additionally, we performed a quantitative evaluation and analysis after applying the Gaussian filter, Wiener filter, and TV noise reduction algorithm to the acquired noisy images.Cylindrical blocks (6 and 2.5 cm in height and diameter, respectively) were designed to fit into the self-produced phantom case.These blocks were engineered to mimic the density of the human brain tissue (Table 1).For printing, we used acrylonitrile butadiene styrene (ABS), wood, and bronze filaments, including XT-CF20, a co-polyester-based carbon fiber composite material.We produced phantom blocks using a 3D printer, employing the same printing process as that used for the case.Figure 2 shows the blueprint and 3D printer outputs of the phantom blocks.We obtained the self-produced phantom CT images to assess the linear attenuation coefficient.As shown in Figure 3, the inserted materials were XT-CF20, wood, air, ABS, and bronze.To simulate CT images under low-dose conditions, noisy images were obtained by adding zero-centered Gaussian noise with intensities of 0.001, 0.005, 0.01, 0.05, and 0.1 using MATLAB software (ver.2023a; MathWorks, Boston, MA, USA).Additionally, we performed a quantitative evaluation and analysis after applying the Gaussian filter, Wiener filter, and TV noise reduction algorithm to the acquired noisy images.

Image Quality Evaluations
To optimize the smoothing factor of the FNLM noise reduction algorithm, we enlarged the region containing cerebrospinal fluid (CSF)-mimicking and tissue-mimicking material for visual evaluation.In this experiment, we used bronze to simulate bone; however, the CT number of bone was measured to be high because of its high density, and the signal fluctuation rate of the relative tissue was not accurately identified.
To quantitatively evaluate the image quality, we calculated the contrast-to-noise ratio (CNR), coefficient of variation (COV), and normalized noise power spectrum (NNPS) [37][38][39][40].We used MATLAB software (ver.2023a) to calculate the quantitative evaluation factors.Figure 4 shows the region of interests (ROIs), in which the yellow and red boxes are the materials and background regions for noise level evaluation, the blue box is the region for visual evaluation, and the white box indicates the region for NNPS evaluation.

Image Quality Evaluations
To optimize the smoothing factor of the FNLM noise reduction algorithm, we enlarged the region containing cerebrospinal fluid (CSF)-mimicking and tissue-mimicking material for visual evaluation.In this experiment, we used bronze to simulate bone; however, the CT number of bone was measured to be high because of its high density, and the signal fluctuation rate of the relative tissue was not accurately identified.
To quantitatively evaluate the image quality, we calculated the contrast-to-noise ratio (CNR), coefficient of variation (COV), and normalized noise power spectrum (NNPS) [37][38][39][40].We used MATLAB software (ver.2023a) to calculate the quantitative evaluation factors.Figure 4 shows the region of interests (ROIs), in which the yellow and red boxes are the materials and background regions for noise level evaluation, the blue box is the region for visual evaluation, and the white box indicates the region for NNPS evaluation.

Image Quality Evaluations
To optimize the smoothing factor of the FNLM noise reduction algorithm, we enlarged the region containing cerebrospinal fluid (CSF)-mimicking and tissue-mimicking material for visual evaluation.In this experiment, we used bronze to simulate bone; however, the CT number of bone was measured to be high because of its high density, and the signal fluctuation rate of the relative tissue was not accurately identified.
To quantitatively evaluate the image quality, we calculated the contrast-to-noise ratio (CNR), coefficient of variation (COV), and normalized noise power spectrum (NNPS) [37][38][39][40].We used MATLAB software (ver.2023a) to calculate the quantitative evaluation factors.Figure 4 shows the region of interests (ROIs), in which the yellow and red boxes are the materials and background regions for noise level evaluation, the blue box is the region for visual evaluation, and the white box indicates the region for NNPS evaluation.The CNR indicates the ratio of contrast and noise in an ROI and the background region of the same image.
where S R and S BK represent the average values of signal intensity in an ROI and background; σ R and σ BK are standard deviations in an ROI and background, respectively.The COV was calculated to compare the degrees of deviation in the obtained phantom images.
where σ R is the standard deviation of signal intensity and µ is the average value in the ROI.
The NNPS parameter analyzes the noise variation in an image over the spatial frequency range of interest.To calculate NNPS, we first converted the noise image to the frequency domain, normalizing the power spectrum to the mean signal, and then averaging the results.The NNPS calculation is based on air.
where I(x, y) denotes the average image intensity; S(x, y) the average background intensity; N x , N y the pixel numbers along the X-and Y-axes; and ∆x, ∆y the pixel sizes along the Xand Y-axes, respectively.

Optimization of the FNLM Noise Reduction Algorithm
We performed a visual evaluation to derive the optimal value of the smoothing factor, which is a parameter of the FNLM noise reduction algorithm.Figure 5 shows the results of the FNLM noise reduction algorithm with various smoothing factors applied to a CT image with added Gaussian noise, with standard deviations of 0.001, 0.005, 0.01, 0.05, and 0.1.In Figure 5, the reason for choosing a low smoothing factor (d = 0.01) and a high smoothing factor (d = 0.50) was to emphasize that a low smoothing factor is insufficient for noise reduction, and that a high smoothing factor effectively reduces noise; however, it results in significant information loss.From the visual evaluation, we observed that the lower the smoothing factor, the more noise remained, and the higher the smoothing factor, the more effectively the noise was reduced.However, as the smoothing factor increased, we observed a loss of edge signal, a blurring effect, and a decrease in contrast between the two materials.At a smoothing factor of 0.50, as shown in Figure 5, we observed that the noise was effectively reduced; however, blurring effects were generated at low noise intensities, and the grid artifacts were enhanced at high noise intensities.
To analyze the performance of the FNLM noise reduction algorithm and optimize the smoothing factor for each noise intensity, we calculated CNR and COV as quantitative evaluation factors.The quantitative evaluation results confirmed that the CSF, gray matter (GM), and white matter (WM) regions showed improved image quality.Figure 6 shows the CNR results in the measured CSF, GM, and WM regions for images with a smoothing factor for which the FNLM noise reduction algorithm increased from 0.01 to 1.00 at various noise intensities.To analyze the performance of the FNLM noise reduction algorithm and optimize the smoothing factor for each noise intensity, we calculated CNR and COV as quantitative evaluation factors.The quantitative evaluation results confirmed that the CSF, gray matter (GM), and white matter (WM) regions showed improved image quality.Figure 6 shows the CNR results in the measured CSF, GM, and WM regions for images with a smoothing factor for which the FNLM noise reduction algorithm increased from 0.01 to 1.00 at various noise intensities.
An analysis of the CNR graph revealed a significant increase in the CNR for the CSF, GM, and WM regions, followed by a decrease in the slope after reaching a certain point, converging to a consistent value.Additionally, we confirmed that as the noise intensity increased, the overall CNR value decreased, and the smoothing factor value of the FNLM noise reduction algorithm increased in the region where the slope became constant.An analysis of the CNR graph revealed a significant increase in the CNR for the CSF, GM, and WM regions, followed by a decrease in the slope after reaching a certain point, converging to a consistent value.Additionally, we confirmed that as the noise intensity increased, the overall CNR value decreased, and the smoothing factor value of the FNLM noise reduction algorithm increased in the region where the slope became constant.
Figure 7 shows the COV results for the measured CSF, GM, and WM regions, where the smoothing factor for the FNLM noise reduction algorithm increased from 0.01 to 1.00 at various noise intensities.By analyzing the COV graph, we observed that the CSF, GM, and WM graphs showed a rapid decrease in slope and then converged to a consistent value.Moreover, as the noise intensity increased, the average COV value increased, and the smoothing factor of the FNLM noise reduction algorithm increased in areas where the slope was constant.When calculating the slope of the CNR graphs, we found that the slope decreased by half when the smoothing factors of the FNLM noise reduction algorithm were set to 0.12, 0.24, 0.33, 0.30, and 0.40, at the noise intensities of 0.001, 0.005, 0.01, 0.05, and 0.1, respectively.Moreover, when calculating the slope of the COV graphs, we confirmed that the slope decreased by half when the smoothing factors of the FNLM noise reduction algorithm were 0.04, 0.07, 0.10, 0.19, and 0.24, at the noise intensities of 0.001, 0.005, 0.01, 0.05, and 0.1, respectively.Therefore, the average values of the smoothing factor, specifically 0.08, 0.16, 0.22, 0.25, and 0.32, at the point where the slopes of the CNR and COV were halved, were derived as the optimized values at the noise intensities of 0.001, 0.005, 0.01, 0.05, and 0.1, respectively.Figure 7 shows the COV results for the measured CSF, GM, and WM regions the smoothing factor for the FNLM noise reduction algorithm increased from 0.01 at various noise intensities.By analyzing the COV graph, we observed that the CS and WM graphs showed a rapid decrease in slope and then converged to a co value.Moreover, as the noise intensity increased, the average COV value increas the smoothing factor of the FNLM noise reduction algorithm increased in areas wh Thus, the optimized smoothing factor value was determined based on the change in the CNR and COV values (slope = 0.01) for CT images with various smoothing factors and noise intensities of 0.001, 0.005, 0.01, 0.05, and 0.1, respectively.In addition, the average values of the CNR and COV were used to set the optimized values of the smoothing factor, ensuring a balance between noise reduction and resolution enhancement.reduction algorithm were 0.04, 0.07, 0.10, 0.19, and 0.24, at the noise intensities of 0.0 0.005, 0.01, 0.05, and 0.1, respectively.Therefore, the average values of the smoothing tor, specifically 0.08, 0.16, 0.22, 0.25, and 0.32, at the point where the slopes of the C and COV were halved, were derived as the optimized values at the noise intensitie 0.001, 0.005, 0.01, 0.05, and 0.1, respectively.

Comparative Evaluation of the FNLM Algorithm and Conventional Noise Reduction Methods
To evaluate the efficacy of the optimized FNLM, we conducted a comparative evaluation with local filtering techniques for noise reduction, such as the Gaussian filter, Wiener filter, and the TV noise reduction algorithm.
Figure 8 shows the CNR results of the optimized FNLM algorithm, local filtering techniques, and the TV noise reduction algorithm for each material.According to the analysis results, the optimized FNLM exhibited superior values across various noise intensities.At a noise intensity of 0.001, the performance order was FNLM, Wiener filter, TV algorithm, Gaussian filter, and noisy image.For all other noise intensities except 0.001, improved results were observed in the order of FNLM, Wiener filter, Gaussian filter, TV algorithm, and noisy image.Particularly, when comparing the noisy image with the optimized FNLM, we confirmed that the CNR value improved by an average factor of about 10.33 times at a noise intensity of 0.001.Additionally, the CNR value improved by approximately 13.77 and 15.13 times at the noise intensities of 0.005 and 0.01, respectively.Finally, we confirmed that the CNR value improved by approximately 9.92 and 8.19 times at the noise intensities of 0.05 and 0.1, respectively (Table 2).Figure 9 presents the COV results of the optimized FNLM algorithm, local filtering techniques, and the TV noise reduction algorithm for each material.The optimized FNLM exhibited superior values across various noise intensities.At a noise intensity of 0.001, the performance order was FNLM, Wiener filter, TV algorithm, Gaussian filter, and noisy image.For all other noise intensities except 0.001, enhanced results were observed in the order of FNLM, Wiener filter, Gaussian filter, TV algorithm, and noisy image.When comparing the noisy image with the optimized FNLM, we confirmed that, on average, the COV value improved by approximately 9.92 and 15.22 times at the noise intensities of 0.001 and 0.005, respectively.Furthermore, at the noise intensities of 0.01 and 0.05, we confirmed enhancements of about 16.01 and 8.26 times, respectively.Moreover, we observed improvements of approximately 8.16 times at a noise intensity of 0.1 (Table 3).comparing the noisy image with the optimized FNLM, we confirmed that, on aver COV value improved by approximately 9.92 and 15.22 times at the noise intens 0.001 and 0.005, respectively.Furthermore, at the noise intensities of 0.01 and 0 confirmed enhancements of about 16.01 and 8.26 times, respectively.Moreover, served improvements of approximately 8.16 times at a noise intensity of 0.1 (Tabl   Figure 10 shows the results of the NNPS after applying the local filtering techniques, the TV noise reduction algorithm, and the optimized FNLM noise reduction algorithm.In all the images, with various noise intensities, the NNPS value gradually decreased with an increase in the spatial frequency.When we used the optimized FNLM algorithm, the gradual decrease in the NNPS was approximately 10 −2 mm 2 compared to that of the noisy image, with an increase in the spatial frequency at the noise intensities of 0.001, 0.005, 0.01, 0.05, and 0.1.

Discussion
In the field of radiology, X-ray-based CT systems play a critical role in non-i medical imaging, facilitating patient diagnosis [41].However, these systems ha lenges such as device quality deterioration, detector performance degradation, an tial patient motion during CT scans, which can lead to diagnostic errors [8].To these issues, various techniques have been proposed in numerous studies, part

Discussion
In the field of radiology, X-ray-based CT systems play a critical role in non-invasive medical imaging, facilitating patient diagnosis [41].However, these systems have challenges such as device quality deterioration, detector performance degradation, and potential patient motion during CT scans, which can lead to diagnostic errors [8].To address these issues, various techniques have been proposed in numerous studies, particularly those focusing on software-based algorithms for CT image processing.However, local filtering techniques and TV noise reduction algorithms are limited in terms of image quality preservation and efficiency [42].To overcome these limitations, an NLM noise reduction algorithm was developed.The NLM noise reduction algorithm achieves interior pixel value equalization while preserving edges by utilizing ROIs and weight calculations based on adjacent pixel intensities and Euclidean distances [4,43].However, the NLM noise reduction algorithm has time constraints because of its computational complexity.To address this computational challenge, we used the FNLM noise reduction algorithm, which reduces computational complexity by transforming the weight calculations from two dimensions to one dimension [22].
In the field of medical imaging, numerous studies have focused on the application of 3D printing technology [44][45][46][47][48][49].Particularly, these studies focused on tools for implantation or invasive procedures in the human body, phantoms for planning surgical operations, and image acquisition precision based on 3D medical images [50][51][52].Despite this progress, research on the printing of phantoms to evaluate image quality has received limited attention.Thus, in this study, we developed a self-produced phantom to evaluate image quality and examined its usefulness in the image quality assessment of medical images.
To assess the effectiveness of the FNLM noise reduction algorithm, a comparative evaluation was conducted using local filtering techniques and a TV noise reduction algorithm.Additionally, a self-produced phantom was fabricated using 3D printing technology.The evaluation focused on noise parameters, including CNR, COV, and NNPS.These parameters are used as critical quantitative metrics for evaluating the efficacy of the noise reduction algorithms.
As a result of the visual comparative evaluation in Figure 5, we found that noise remained when low smoothing factor values were applied.Moreover, we observed that as the smoothing factor increased significantly, noise was effectively reduced; however, blurring artifacts were generated at low noise intensities and grid artifacts were intensified at high noise intensities.Furthermore, the contrast between the CSF and the tissue decreased as the smoothing factor increased because, as the smoothing factor increases, the interference between the signals of the two tissues increases due to excessive smoothing from the increased distance weight of the FNLM algorithm.Consequently, the signals of other tissues are invaded, resulting in the loss of high-frequency information in some areas, and the difference in signal values between the CSF and tissue parts becomes similar.
The CNR and COV graphs indicated a higher contrast improvement and noise reduction efficiency as the slope changes rapidly.Based on these tendencies, we identified regions where the contrast was reduced by blending the signals from the two different tissues using the CNR measurement results.In addition, the COV results showed regions where the blurring effect had a greater impact on the image than noise reduction.To derive the optimized smoothing factor for CNR and COV, we considered the region where the slope decreased by more than half (where the improvement rate dropped sharply).Subsequently, to balance noise reduction and contrast, the optimization of the FNLM noise reduction algorithm was set to the mean value of the optimized smoothing factor values measured in the CNR and COV.In addition, we observed that the degree of improvement in image quality decreased as the noise intensity increased, and we identified an increase in the value of the smoothing factor at points with a consistent slope.Consequently, the optimized smoothing factors for the FNLM noise reduction algorithm were determined to be 0.08, 0.16, 0.22, 0.25, and 0.32 for the CT images with added Gaussian noise intensities of 0.001, 0.005, 0.01, 0.05, and 0.1, respectively.
Based on these results, we derived the optimized values for the smoothing factor of the FNLM algorithm and conducted a quantitative comparative evaluation of the images using the optimized smoothing factor, local filtering techniques, and the TV noise reduction algorithm.After applying the optimized FNLM noise reduction algorithm at a noise intensity of 0.005, the CNR values in various ROIs improved by 6.55 to 10.97 times, and the COV values improved by 6.66 to 13.33 times.Moreover, at a noise intensity of 0.01, the CNR values improved by approximately 6.85 to 13.80 times, and the COV values improved by 6.20 to 15.19 times.At a noise intensity of 0.1, the CNR values improved by 3.58 to 10.02 times, and the COV values improved by 3.92 to 7.74 times.In addition, the NNPS of the image subjected to the optimized FNLM noise reduction algorithm improved by approximately 10 −2 mm 2 compared to that of the noisy image at the noise intensities of 0.001, 0.005, 0.01, 0.05, and 0.1.Numerous studies have been conducted on the FNLM noise reduction algorithm, with a primary focus on improving image quality.Therefore, our results indicate that the FNLM noise reduction algorithm is effective in reducing noise in CT images and outperforms local noise reduction algorithms under low-dose settings with high noise levels.Additionally, the FNLM noise reduction algorithm effectively enhanced the CNR and COV in the CSF, GM, and WM regions, regardless of the noise intensity.
In our study, we fabricated a phantom with the approximate dimensions of a human head using a 3D printer by employing filaments composed of various materials to simulate human tissues.Subsequently, we quantitatively evaluated the FNLM noise reduction algorithm using the CNR, COV, and NNPS parameters, which reflect both noise and image quality of a self-produced phantom image.A limitation of this study is that the bone region was not evaluated; a self-produced phantom block was produced using bronze to mimic bone material, but the signal was too strong to measure.In addition, the bronze block caused metallic artifacts because of its high density, which may have affected the performance of the local filtering techniques, TV noise reduction algorithm, and FNLM noise reduction algorithm.To demonstrate the performance of the FNLM denoising algorithm, a quantitative evaluation was conducted by setting up ROIs to minimize the effects of metallic artifacts.Although the results of this study demonstrate that the FNLM algorithm has useful denoising efficiency, we plan to fabricate other blocks that can better simulate bone material and to conduct a phantom study that includes bone parts in the future to achieve more accurate results.
Our study demonstrated the effectiveness of the FNLM noise reduction algorithm for CT noise reduction and significant image quality enhancement.In the clinical field, low-dose CT has been used to address the issue of radiation exposure.However, lowdose CT scans inevitably introduce noise because of an insufficient number of photons during image acquisition [53,54].Based on the results of our study, we anticipate that the FNLM algorithm can effectively reduce the noise generated in low-dose CT images, thereby significantly reducing radiation exposure.
Recently, an adaptive non-local means (ANLM) algorithm has been proposed, which improves on the traditional NLM by dynamically adjusting parameters based on noise characteristics [55].Compared to the traditional NLM algorithm, which requires the manual optimization of the smoothing factor, the ANLM algorithm automatically detects the noise characteristics and dynamically adjusts parameters such as the smoothing factor and search window size.This allows the ANLM algorithm to automatically derive optimized values and perform more flexibly and effectively under various noise conditions.Although previous studies have demonstrated the efficiency of the ANLM algorithm, there is limited research comparing the performance of the ANLM algorithm and the FNLM algorithm.Therefore, a comparative performance study between the optimized smoothing factor of the FNLM algorithm and the automatic optimization technique of the ANLM is needed to identify the advantages and disadvantages of each in various noise conditions.
Additionally, this study suggests the possibility of improving medical imaging processes using 3D printing, leading to higher diagnostic accuracy.Traditional 3D printing techniques have been used in certain parts of the medical field, including procedural tools, assistive devices, and implants [56][57][58][59][60].However, this study demonstrates the feasibility of applying 3D printer-based phantoms in the field of medical image processing.Moreover, the 3D printing technique offers significant advantages in terms of cost effectiveness and reproducibility, making it suitable for mass production [61][62][63][64].Because of these advantages, the application of 3D printing in deep learning is also feasible [65,66].Our study highlights several advantages of using denoised images to construct a deep learning dataset.Denoised images offer improved quality, enhancing the accuracy of deep learning model training and the generalization capability of these models [67][68][69].Using 3D-printing phantoms to build datasets for deep learning can minimize ethical concerns compared to using patient data.Specifically, using phantoms to acquire images avoids issues related to patient privacy and reduces radiation exposure, which are significant ethical considerations.Furthermore, 3D-printing phantoms provide repeatability and reproducibility, making them suitable for QC purposes.Our study results show that the integration of 3D printing and phantom fabrication techniques has the potential to create innovative technologies and algorithms to improve medical image quality.This approach addresses the ethical issues of data scarcity and radiation exposure, as well as leveraging the consistent and controllable characteristics of phantoms to generate high-quality datasets for deep learning applications.Therefore, we expect that when 3D printing technology is properly utilized in medical imaging studies, it will contribute to the improvement of medical imaging quality, as well as the advancement of deep learning technology.

Conclusions
In this study, we modeled and applied the FNLM noise reduction algorithm to reduce noise in medical images acquired from CT systems.To evaluate image quality, we fabricated a self-produced phantom using a 3D printer.In addition, we conducted a quantitative analysis by comparing the FNLM algorithm with local filtering techniques and the TV noise reduction algorithm to confirm the effectiveness of the FNLM noise reduction approach.In the phantom study, we confirmed considerable improvements across all quantitative evaluation factors with the implementation of the FNLM noise reduction algorithm, surpassing the performances of local filtering techniques and the TV noise reduction algorithm.These results suggest that the FNLM algorithm can effectively replace local filtering techniques and the TV noise reduction algorithm.Furthermore, this study demonstrates that self-produced phantoms using 3D printers can be adaptively applied in the medical image processing field.

Figure 1 .
Figure 1.Components of the 3D printer based on the fused filament fabrication technique.Figure 1. Components of the 3D printer based on the fused filament fabrication technique.

Figure 1 .
Figure 1.Components of the 3D printer based on the fused filament fabrication technique.Figure 1. Components of the 3D printer based on the fused filament fabrication technique.

Figure 2 .
Figure 2. Image for manufacturing of (a) a blueprint of a block, (b) blueprint of a case, and (c) printed self-produced phantom.

Figure 2 .
Figure 2. Image for manufacturing of (a) a blueprint of a block, (b) blueprint of a case, and (c) printed self-produced phantom.

Figure 4 .
Figure 4. Region of interests (ROIs) setup and backgrounds for quantitative and visual evaluation.

Figure 4 .
Figure 4. Region of interests (ROIs) setup and backgrounds for quantitative and visual evaluation.Figure 4. Region of interests (ROIs) setup and backgrounds for quantitative and visual evaluation.

Figure 4 .
Figure 4. Region of interests (ROIs) setup and backgrounds for quantitative and visual evaluation.Figure 4. Region of interests (ROIs) setup and backgrounds for quantitative and visual evaluation.

Figure 5 .
Figure 5.The results are magnified regions of Figure 4, using the fast non-local means (FNLM) noise reduction algorithm with various smoothing factors () on a computed tomography (CT) image with Gaussian noise added with a standard deviation: (a) low smoothing factor, (b) semi-low smoothing factor, (c) optimized smoothing factor, (d) semi-high smoothing factor, and (e) high smoothing factor.

Figure 5 .
Figure 5.The results are magnified regions of Figure 4, using the fast non-local means (FNLM) noise reduction algorithm with various smoothing factors (d) on a computed tomography (CT) image with Gaussian noise added with a standard deviation: (a) low smoothing factor, (b) semi-low smoothing factor, (c) optimized smoothing factor, (d) semi-high smoothing factor, and (e) high smoothing factor.

Diagnostics 2024 ,Figure 8 .
Figure 8. Comparative contrast-to-noise ratio (CNR) evaluation results of optimized fast n means (FNLM), local filtering techniques, and total-variation (TV) noise reduction algorithm produced phantom with various noise intensities: (a) 0.001, (b) 0.005, (c) 0.01, (d) 0.05, and ( Figure 9 presents the COV results of the optimized FNLM algorithm, local f techniques, and the TV noise reduction algorithm for each material.The optimized exhibited superior values across various noise intensities.At a noise intensity of 0.0 performance order was FNLM, Wiener filter, TV algorithm, Gaussian filter, and no age.For all other noise intensities except 0.001, enhanced results were observed order of FNLM, Wiener filter, Gaussian filter, TV algorithm, and noisy image.

Table 1 .
Attenuation coefficient of the reference tissue and filament materials.

Table 1 .
Attenuation coefficient of the reference tissue and filament materials.