Noise Level and Similarity Analysis for Computed Tomographic Thoracic Image with Fast Non-Local Means Denoising Algorithm

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Article Noise Level and Similarity Analysis for Computed Tomographic Thoracic Image with Fast Non-Local Means Denoising Algorithm

Bae-Guen Kim 1 , Seong-Hyeon Kang 1, Chan Rok Park 2, Hyun-Woo Jeong 3,* and Youngjin Lee 1,*

1 Department of Radiological Science, Gachon University, 191, Hambakmoero, Yeonsu-gu, Incheon 21936, Korea; [email protected] (B.-G.K.); [email protected] (S.-H.K.) 2 Department of Radiological Science, Jeonju University, 303, Cheonjam-ro, Wansan-gu, Jeonju-si 55069, Korea; [email protected] 3 Department of Biomedical Engineering, Eulji University, 553, Sanseong-daero, Sujeong-gu, Seongnam-si, Gyeonggi-do 13135, Korea * Correspondence: [email protected] (H.-W.J.); [email protected] (Y.L.); Tel.: +82-31-740-7135 (H.-W.J.); +82-32-820-4362 (Y.L.) Received: 14 September 2020; Accepted: 21 October 2020; Published: 23 October 2020

Abstract: Although conventional denoising filters have been developed for noise reduction from digital images, these filters simultaneously cause blurring in the images. To address this problem, we proposed the fast non-local means (FNLM) denoising algorithm which would preserve the edge information of objects better than conventional denoising filters. In this study, we obtained thoracic computed tomography (CT) images from a male adult mesh (MASH) phantom modeled by computer and a five-year-old phantom to perform both the simulation study and the practical study. Subsequently, the FNLM denoising algorithm and conventional denoising filters, such as the Gaussian, median, and Wiener filters, were applied to the MASH phantom image adding Gaussian noise with a standard deviation of 0.002 and practical CT images. Finally, the results were compared quantitatively in terms of the coefficient of variation (COV), contrast-to-noise ratio (CNR), peak signal-to-noise ratio (PSNR), and correlation coefficient (CC). The results showed that the FNLM denoising algorithm was more efficient than the conventional denoising filters. In conclusion, through the simulation study and the practical study, this study demonstrated the feasibility of the FNLM denoising algorithm for noise reduction from thoracic CT images.

Keywords: noise analysis; computed tomography thoracic image; fast non-local means approach; denoising algorithm; MASH phantom

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].

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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 [7–9]. 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]. Naegelad 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 [14–18]. 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.

2. Materials and Methods

2.1. Acquisition of the Thoracic Image from the Male Adult Mesh (MASH) Phantom: The Simulation Study The MASH phantom is a computational model of human anatomy for research in medicine and radiology. These phantoms are realized using the polygon mesh technique, which uses a collection of vertices, edges, and faces to deﬁne the shape of a polyhedral object with three-dimensional (3D) computer graphics. The MASH phantom is more similar to the human body than the conventional medical internal radiation dose (MIRD5) phantom. The advantages of using the MASH phantom are that variables corresponding to changes in the posture of the human body and irradiation conditions can be controlled, along with preventing patient/subject exposure. The MASH phantom was designed to represent the standing position of a male adult with 113 organs, bones, and tissues according to the recommendations of report 89 of the ICRP. The pixelized phantom shows 97.4% consistency with the ICRP data [19–21]. This image processing was performed using MATLAB (version R2020a, The MathWorks, Inc., Natick, MA, USA). An axial thoracic image was obtained from the CT scan dataset of the MASH phantom. Then, Gaussian noise with a standard deviation of 0.002 was added to the image. Figure1 Appl. Sci. 2020, 10, 7455 3 of 14

Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 14 showsAppl. the Sci. original 2020, 10, x thoracic FOR PEER imageREVIEW with the target and background ROIs. The region within3 of the 14 blue shows the original thoracic image with the target and background ROIs. The region within the blue box was magniﬁed to highlight the reconstruction results. ROItarget and ROIbackground were set over the cardiacshowsbox and was the lung magnified original regions, thoracic to highlight respectively. image the with reconstruction the target and results. background ROItarget ROIs.and ROI Thebackground region were within set overthe blue the cardiac and lung regions, respectively. box was magnified to highlight the reconstruction results. ROItarget and ROIbackground were set over the cardiac and lung regions, respectively.

FigureFigure 1. The 1. The image image obtained obtained from from the the male male adultadult mesh (MASH) (MASH) phantom. phantom. The The region region inside inside the blue the blue box wasFigurebox magnifiedwas 1. magnified The image to compareto obtained compare thefrom the denoised thedenoised male adult images. images. mesh Re Regions (MASH)gions of of interestsphantom. interests (ROIs) The (ROIs) region were were setinside to set calculate the to blue calculate the coeboxtheffi coefficientwascient magnified of variation of variation to compare (COV) (COV) the and and denoised contrast contrast images. to to noisenoise Re ratio gions (CNR) (CNR)of interests of of the the (ROIs)obtained obtained were chest set chest image.to calculate image. the coefficient of variation (COV) and contrast to noise ratio (CNR) of the obtained chest image. 2.2. Acquisition2.2. Acquisition of the of the Thoracic Thorac Imageic Image from from the the Five-Year-Old Five-Year-Old Phantom: Phantom: The The Practical Practical Study Study 2.2. Acquisition of the Thoracic Image from the Five-Year-Old Phantom: The Practical Study A 5-year-oldA 5-year-old phantom phantom (Model (Model ATOM ATOM 704,704, CIRSCIRS Inc., Inc., Norfolk, Norfolk, VA, VA, USA) USA) was was scanned scanned using using a a 64-detector64-detectorA row5-year-old scannerrow scannerphantom (SOMATOM (SOMATOM (Model Definition ATOM Definition 704, AS CIRS+, Siemens,AS+, Inc., Siemens,Norfolk, Malvern, VA,Malver PA,USA)n, USA). wasPA, ThescannedUSA). CT The examinationusing CT a examination parameters were set as follows: tube potential, 120 kVp; tube current, 23 mA; exposure parameters64-detector were row set asscanner follows: (SOMATOM tube potential, Definition 120 kVp; AS+, tube Siemens, current, Malver 23 mA;n, PA, exposure USA). time,The CT 300 ms; time, 300 ms; and slice thickness, 1 mm. Then, the axial image of 512 × 512 size was obtained. and sliceexamination thickness, parameters 1 mm. Then, were theset axialas follows: image tube of 512 potential,512 size120 kVp; was obtained.tube current, Generally, 23 mA; exposure the low-dose time,Generally, 300 ms; the low-doseand slice CTthickness, examinations 1 mm. are Then, perfor themed× axial with image 30–50 ofmAs. 512 However, × 512 size in wasthis study,obtained. the CT examinations are performed with 30–50 mAs. However, in this study, the parameters of 7 mAs Generally,parameters the of low-dose7 mAs were CT setexaminations in order to are show perfor thatmed the withFNLM 30–50 denoising mAs. However, algorithm in was this efficient study, the at were set in order to show that the FNLM denoising algorithm was efficient at low exposure conditions. parameterslow exposure of conditions.7 mAs were Moreover, set in order in modernto show CT that examination, the FNLM denoising the automatic algorithm current was technique efficient has at Moreover,lowbeen exposure utilized in modern toconditions. compensate CT examination, Moreover, the differences thein modern automatic of thicknessCT examination, current of body. technique the However, automatic has been in currentthis utilized examination, technique to compensate hasthe the dibeenfixedfferences utilizedcurrent of towas thickness compensate utilized of to body.the show differences However,the clear of results inthickness this by examination, excluding of body. However,some the random fixed in thiscurrent parameters. examination, was In utilized thisthe to showfixedexperiment, the clearcurrent results we was did utilized by not excluding add to showthe Gaussian some the clear random noise results parameters.to bythe excludingimage Inthat thissome we experiment, obtainedrandom parameters.to derive we did practical notIn this add the Gaussianexperiment,results noise from to anwe the unaffecteddid image not add that condition. the we Gaussian obtained Figure noise 2 to show derive to sthe thepractical image initiative that results image we obtained of from the an5-year-old to una deriveffected phantom. practical condition. FigureresultsThe2 shows ROIs from and the an blue initiativeunaffected box in image condition. the image of the Figure were 5-year-old 2set show as sthe phantom.the similar initiative regions The image ROIs to of the andthe image5-year-old blue of box the phantom. in MASH the image phantom. wereThe set asROIs the and similar blue regions box in tothe the image image were of set the as MASH the similar phantom. regions to the image of the MASH phantom.

Figure 2. The image obtained from a 5-year-old phantom. The region inside the blue box was magniﬁed

to compare the denoised images. ROIs were set to calculate the coeﬃcient of variation (COV) and contrast-to-noise ratio (CNR) of the chest image. Appl. Sci. 2020, 10, 7455 4 of 14

2.3. Fast Non-Local Means Algorithm The NLM denoising algorithm is effective for noise reduction. In addition, this algorithm can resolve the problems of conventional denoising filters, such as signal distortion and blurring. This is because the NLM denoising algorithm compares the overall geometric composition using the Euclidean distance as a weight as opposed to using the sliding method on the entire image, such as in the case of the Gaussian, median, and Wiener filters. The NLM denoising algorithm can be defined as follows: X NL[I](m) = ω(m, n)I(n), (1) N I ∈ where the weight ω(m, n) is defined as follows:

2 Gσ(τ) I(M+τ) I(n+τ) 1 X k − k2 ω(m, n) = e− d2 , (2) Z(m)

2 where τ is the number of pixels ; Gσ(τ) is the Gaussian distribution with size σ of the number of background pixels; I(M + τ) I(n + τ) 2 is the intensity diﬀerence between adjacent pixels based on k − k2 the Euclidean distance values; and Z(m) sets the leveling constant, as follows:

2 Gσ(τ) I(m+τ) I(n+τ) X k − k2 Z(m) = e− d2 . (3) n

The FNLM denoising algorithm modifies the calculation of ω(m, n) in the NLM denoising algorithm from one dimension to two dimensions. The modified ω(m, n) is defined as follows:

1 ω(m, n) = H (I(m + s) I(m s)), (4) Z(m) i − − where τ is defined as n m, s is defined as m + τ, and H is defined as follows: − i

I(q) I(q+τ) 2 Xs k − k2 2 Hi(s) = e− d . (5) q=0

Compared with the NLM denoising algorithm, the FNLM denoising algorithm theoretically improves the time resolution by approximately 4 by simplifying the process through one-dimensional × computations [12–18,22].

2.4. Quantitative Evaluation Factors

2.4.1. Evaluation Factors for the Noise Level In this study, noise leveling factors such as the coeﬃcient of variation (COV) and contrast-to-noise ratio (CNR) were employed [23,24]. ROIs were set to calculate the COV (using the target ROI) and CNR (using the target and background ROIs). The COV is an evaluation factor that quantitatively represents the noise in an image. A superior image has a low COV. In addition, the CNR is a factor that evaluates the contrast and noise of images in combination. A superior image has a high CNR. The COV and CNR are deﬁned as follows: σ COV = , (6) µ

S S CNR = A B q| − | , (7) 1 2 + 2 2 σA σB Appl. Sci. 2020, 10, 7455 5 of 14

where σ is the standard deviation of the signal ; µ is the mean value of the signal ; SA and σA are the mean and standard deviation of the signal in the target ROI, respectively; and SB and σB are the average and standard deviation of the background signal, respectively.

2.4.2. Evaluation Factors for Similarity The peak signal-to-noise ratio (PSNR) and correlation coefficient (CC) were used to evaluate the similarity [25,26]. A superior image has a high PSNR, which is primarily used to evaluate the loss of image quality. However, the PSNR of lossless image is undefined because its mean squared error (MSE) is 0. In addition, CC represents the relationship between the original and denoised images and assumes values in the range of 1 to +1, where 1 indicates the strongest possible concordance and 0 − ± the strongest possible discordance. The CC is equal to the ratio of the covariance and the product of the standard deviations of original and denoised images. The PSNR and CC are defined as follow:

MAX2 PSNR = 10 log ( I ), (8) × MSE

Pn i Xi X Yi Y CC = q − q − , (9) P 2 P 2 n X X n Y Y i i − i i − where MAXI in Equation (8) is the maximum signal value and MSE is deﬁned as follow:

N M 1 X X 2 MSE = [I(i, j) In(i, j)] , (10) M N − × i=1 j=1 where I is a grayscale image with a size of M N size and In is the noisy image. × 3. Results

3.1. Results from MASH Phantom Figure3 shows the region inside the blue box that was magnified to clearly illustrate the performance of each noise reduction algorithm. The original (top left, Figure3), noisy (top right, Figure3), Gaussian (center left, Figure3), median (center right, Figure3), Wiener (bottom left, Figure3), and FNLM (bottom right, Figure3) images are depicted. We performed qualitative visual evaluation of the images obtained by applying the conventional denoising filters and FNLM denoising algorithm. Subsequently, the performance of the FNLM denoising algorithm was evaluated in terms of various quantitative evaluation factors. Figure4 shows the COV and CNR results for evaluating the noise level of the reconstructed images. In the noise level evaluation, the FNLM denoising algorithm achieved the best performance as compared with the conventional denoising filters. The COV values of images applied the noisy, Gaussian, median, Wiener, and proposed FNLM denoising algorithm were 0.237, 0.154, 0.087, 0.046, and 0.023, respectively. The COV of the image obtained with the FNLM denoising algorithm was approximately 10.3 , 6.7 , 3.8 , and 2.02 higher than that of the noisy, Gaussian, median, and Wiener × × × × images, respectively. Moreover, the CNRs of the noisy, Gaussian, median, Wiener, and proposed FNLM denoising algorithm were 4.908, 7.600, 11.947, 25.511, and 55.627, respectively. The CNR of the image obtained with the FNLM denoising algorithm was approximately 11.33 , 7.32 , 4.66 , and 2.18 × × × × higher than that of the noisy, Gaussian, median, and Wiener images, respectively. Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 14

Appl.respectively. Sci. 2020, 10 Unlike, 7455 the PSNR results, the FNLM denoising algorithm had the highest CC value,6 of 14 followed by the Wiener, median, Gaussian, and noisy images.

Figure 3. Magnified views (region inside the blue box). (a) Original; (b) Noisy; (c) Gaussian filtered; (Figured) Median 3. Magnified filtered; ( eviews) Wiener (region filtered; inside (f) the Fast blue non-local box). ( meansa) Original; (FNLM) (b) filteredNoisy; ( images.c) Gaussian filtered; (d) Median filtered; (e) Wiener filtered; (f) Fast non-local means (FNLM) filtered images. Figure5 shows the PSNR and CC results for evaluating the similarity between the original and reconstructed images. In the similarity evaluation, the FNLM denoising algorithm again showed the most efficient value as compared with the conventional denoising filters. The PSNRs of the noisy, Gaussian, median, Wiener, and proposed FNLM denoising algorithm were 77.261, 79.537, 82.094, 81.882, and 82.354, respectively. The FNLM denoising algorithm had the highest PSNR, followed by the median, Wiener, Gaussian, and noisy images. Moreover, the CC values of the noisy, Gaussian, median, Wiener, and proposed FNLM denoising algorithm were 0.958, 0.977, 0.985, 0.990, and 0.990, respectively. Unlike the PSNR results, the FNLM denoising algorithm had the highest CC value, followed by the Wiener, median, Gaussian, and noisy images.

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Figure 4. The (a) coefficient of variation (COV) and (b) contrast-to-noise ratio (CNR) metrics Figure 4. The (a) coe cient of variation (COV) and (b) contrast-to-noise ratio (CNR) metrics computed computed in the setﬃ ROIs to evaluate the noise level of the reconstructed image obtained from the inFigure the set 4. ROIs The to(a evaluate) coefficient the noise of variation level of the (COV) reconstructed and (b image) contrast-to-noise obtained from ratio the MASH (CNR) phantom. metrics MASH phantom. computed in the set ROIs to evaluate the noise level of the reconstructed image obtained from the MASH phantom.

Figure 5. The (a) peak signal-to-noise ratio (PSNR) and (b) correlation coeﬃcient (CC) values used to evaluateFigure 5. theThe similarity (a) peak signal-to-nois between the reconstructede ratio (PSNR) images and (b and) correlation original image.coefficient (CC) values used to evaluate the similarity between the reconstructed images and original image. Figure 5. The (a) peak signal-to-noise ratio (PSNR) and (b) correlation coefficient (CC) values used to evaluate the similarity between the reconstructed images and original image.

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Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 3.2. Results from the Five-Year-Old Phantom 3.2. Results from the Five-Year-Old Phantom Figure6 shows the region inside the blue box that was magnified to clearly illustrate the performance Figure 6 shows the region inside the blue box that was magnified to clearly illustrate the of each noise reduction algorithm. The original (top left, Figure6a), Gaussian (top center, Figure6a), performance of each noise reduction algorithm. The original (top left, Figure 6a), Gaussian (top center, median (top right, Figure6c), Wiener (bottom left, Figure6d), and FNLM (bottom right, Figure6e) Figure 6a), median (top right, Figure 6c), Wiener (bottom left, Figure 6d), and FNLM (bottom right, images are depicted. There was not any additional noise except for the natural noise of the image Figure 6e) images are depicted. There was not any additional noise except for the natural noise of the acquisition process. As a result of observing the images of Figure6, the image in Figure6e was the image acquisition process. As a result of observing the images of Figure 6, the image in Figure 6e was clearest. Subsequently, the performance of the FNLM denoising algorithm was evaluated in terms of the clearest. Subsequently, the performance of the FNLM denoising algorithm was evaluated in terms the two noise level evaluation factors. of the two noise level evaluation factors.

Figure 6. Magnified views (region inside the blue box). (a) Original; (b) Gaussian filtered; (c) Median Figure 6. Magnified views (region inside the blue box). (a) Original; (b) Gaussian filtered; (c) Median filtered; (d) Wiener filtered; (e) FNLM filtered images. filtered; (d) Wiener filtered; (e) FNLM filtered images. Figure7 shows the COV and CNR results for evaluating the noise level of the reconstructed imagesFigure of the 7 shows five-year-old the COV phantom. and CNR Inresults the noise for evaluating level evaluation the noise of level these of images, the reconstructed the FNLM denoisingimages ofalgorithm the five-year-old achieved thephantom. best performance In the no asise compared level evaluation with the conventionalof these images, denoising the FNLM filters. Thedenoising acquired algorithm COV values achieved of images the best applied performance the original, as compared Gaussian, wi median,th the conventional Wiener, and denoising proposed FNLMfilters. The denoising acquired algorithm COV values were 0.000798,of images 0.000751, applied 0.000703,the original, 0.000497, Gaussian, and 0.000102,median, Wiener, respectively. and Theproposed COVs ofFNLM the images denoising obtained algorithm with the were FNLM 0.000798 denoising, 0.000751, algorithm 0.000703, were approximately 0.000497, and 7.82 0.000102,, 7.36 , × × 6.89respectively., and 4.87 Thebetter COVs than of that the of images the original, obtain Gaussian,ed with median,the FNLM and Wienerdenoising images, algorithm respectively. were × × Moreover,approximately the CNRs7.82×, 7.36×, of the 6.89×, original, and Gaussian,4.87× better median, than that Wiener, of the andoriginal, proposed Gaussian, FNLM median, denoising and algorithmWiener images, were 45.138,respectively. 47.630, Moreover, 50.527, 67.125, the CNRs and of 236.635, the original, respectively. Gaussian, The median, CNRs ofWiener, the image and obtainedproposed withFNLM the denoising FNLM denoising algorithm algorithm were 45.138, were 47 approximately.630, 50.527, 67.125, 5.24 and, 4.97 236.635,, 4.68 respectively., and 3.53 × × × × higherThe CNRs than of that the of image the original, obtained Gaussian, with the median, FNLM and denoising Wiener algorithm images, respectively. were approximately 5.24×, 4.97×, 4.68×, and 3.53× higher than that of the original, Gaussian, median, and Wiener images, respectively.

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Figure 7. The (a) coefficient of variation (COV) and (b) contrast-to noise-ratio (CNR) metrics computed in theFigure set ROIs 7. The to evaluate (a) coefficient the noise of level variation of the reconstructed (COV) and image(b) contrast-to obtained from noise-ratio the 5-year-old (CNR) phantom. metrics computed in the set ROIs to evaluate the noise level of the reconstructed image obtained from the 5- 4. Discussion year-old phantom. Lung cancer consistently has the highest mortality rate among cancers. Therefore, early diagnosis through4. Discussion regular monitoring using CT is critical to decrease the death rate, which has also been proven to work in practice. Unfortunately, CT, which is based on X-rays, is accompanied by potential risks Lung cancer consistently has the highest mortality rate among cancers. Therefore, early because of its high-dose exposure. Meanwhile, it is important to find the peripheral lung nodules as diagnosis through regular monitoring using CT is critical to decrease the death rate, which has also they can become cancerous. Recently, the feasibility of using low-dose examination for the discovery been proven to work in practice. Unfortunately, CT, which is based on X-rays, is accompanied by of peripheral lung nodules has been demonstrated and various studies have showen that low-dose potential risks because of its high-dose exposure. Meanwhile, it is important to find the peripheral examination can replace the conventional methods [27–29]. The exposure dose of the subjects can be lung nodules as they can become cancerous. Recently, the feasibility of using low-dose examination significantly reduced by low-dose examination. for the discovery of peripheral lung nodules has been demonstrated and various studies have showen However, low-dose examination inevitably leads to a large amount of noise caused by scattering that low-dose examination can replace the conventional methods [27–29]. The exposure dose of the rays, leading to misdiagnosis in some cases. Accordingly, several algorithms have been developed subjects can be significantly reduced by low-dose examination. to reduce the noise. However, conventional local denoising filters cause blurring of the edges in the However, low-dose examination inevitably leads to a large amount of noise caused by scattering images. To address this problem, a non-local algorithm was selected in this study. rays, leading to misdiagnosis in some cases. Accordingly, several algorithms have been developed to The purpose of this study was to demonstrate the feasibility of the FNLM denoising algorithm for reduce the noise. However, conventional local denoising filters cause blurring of the edges in the noise reduction from thoracic CT scans. In the first process of this experiment, axial thoracic images images. To address this problem, a non-local algorithm was selected in this study. were obtained from CT data of a MASH phantom using the MATLAB program, and then Gaussian noise The purpose of this study was to demonstrate the feasibility of the FNLM denoising algorithm with a standard deviation of 0.002 was added to these axial thoracic images. The Gaussian-Poisson for noise reduction from thoracic CT scans. In the first process of this experiment, axial thoracic mixture is general noise in the images based on X-ray [30]. The reason why the Poisson was not images were obtained from CT data of a MASH phantom using the MATLAB program, and then considered in this study is that the Poisson noise is affected by the modalities. It is usually caused Gaussian noise with a standard deviation of 0.002 was added to these axial thoracic images. The due to the lack of photons. Therefore, we considered the Gaussian noise that represents the normal Gaussian-Poisson mixture is general noise in the images based on X-ray [30]. The reason why the distribution overall. The Gaussian, median, Wiener, and FNLM denoising algorithms were, then, Poisson was not considered in this study is that the Poisson noise is affected by the modalities. It is applied to the noisy images. Subsequently, the filtering results were compared using quantitative usually caused due to the lack of photons. Therefore, we considered the Gaussian noise that evaluation factors. Here, COV and CNR were used to evaluate the degree of noise after application represents the normal distribution overall. The Gaussian, median, Wiener, and FNLM denoising of the algorithms. Actually, there are a few methodologies for noise estimation [31]. In this study, algorithms were, then, applied to the noisy images. Subsequently, the filtering results were compared the general method that calculates the variation of pixel values of the region that is composed of the using quantitative evaluation factors. Here, COV and CNR were used to evaluate the degree of noise same matter was utilized. The variation can be considered to be noise because the pixel values of the after application of the algorithms. Actually, there are a few methodologies for noise estimation [31]. In this study, the general method that calculates the variation of pixel values of the region that is

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Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 14 same matter should be the same. Continuously, the PSNR was used to assess the amount of image qualitycomposed loss,and of the the same CC was matter used was to evaluateutilized. theThe correlationvariation can between be considered the images. to be Next, noise the because image the from thepixel five-year-old values of the phantom same matter was obtained should be under the sa practicalme. Continuously, conditions the to PSNR verify was whether used to the assess proposed the amount of image quality loss, and the CC was used to evaluate the correlation between the images. algorithm could be used in the clinical field or not. Next, the image from the five-year-old phantom was obtained under practical conditions to verify The process of selecting a phantom and the characteristics of lung cancer, such as gender and age, whether the proposed algorithm could be used in the clinical field or not. were not considered, because we focused on demonstrating the performances about noise reduction The process of selecting a phantom and the characteristics of lung cancer, such as gender and and edge information preservation. We supposed that according to the hypothesis associated with age, were not considered, because we focused on demonstrating the performances about noise thereduction relationship and between edge information the density preservation. and the attenuation, We supposed this phantom that according that has to similar the hypothesis composition withassociated human anatomywith the canrelationship derive useful between results the [densi32,33ty]. However,and the attenuation, for more reliable this phantom results, that utilizing has a phantomsimilar thatcomposition is similar with to the human MASH anatomy phantom can is ideal.derive The useful process results of this[32,33]. experiment However, is thefor samemore as thereliable process results, of the first.utilizing However, a phantom we didthat not is similar add the to Gaussian the MASH noise phantom and evaluated is ideal. The the process noise level of this only. Asexperiment shown by theis the results, same as the the proposed process of FNLM the first denoising. However, algorithm we did not showed add the the Gaussian best performance noise and in everyevaluated evaluation the noise regardless level only. of the As virtual shown and by practicalthe results, image. the proposed FNLM denoising algorithm showedAlthough, the best originally, performance the PSNR in every was evaluation optimized regardless to evaluate of the the virtua qualityl and of thepractical compressed image. image, in this study,Although, the originally, PSNR was the used PSNR to was evaluate optimized the degree to evaluate of image the quality restoration of the achievedcompressed by image, various denoisingin this study, algorithms. the PSNR The was PSNR used and to evaluate CC values the candegree diff erof fromimage visual restoration evaluation, achieved as theseby various factors aredenoising measured algorithms. mathematically. The PSNR However, and CC as values shown can in differ Figures from3 and visual6, theevaluation, image that as these was thefactors applied are FNLMmeasured denoising mathematically. algorithm visuallyHowever, showed as shown the in clearest Figures image 3 and without6, the image any blurring.that was the To proveapplied the enhancementFNLM denoising of noise algorithm level and visually sharpness, showed we the measured clearest theimage signal without intensity any blurring. of the images. To prove Figures the 8 andenhancement9 show the signalof noise intensity level and profiles sharpness, of the we imagesmeasured that the are signal the appliedintensity Wienerof the images. filter and Figures FNLM 8 denoisingand 9 show algorithm, the signal respectively. intensity profiles The Wiener of the filter,images only, that was are the analyzed applied to Wiener compare filter with and the FNLM 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 denoising algorithm because the Wiener filter showed the best performance in almost all of the evaluations among the conventional denoising filters. evaluations among the conventional denoising filters. Figure8 is the signal intensity profile of the image that was obtained from the MASH phantom. 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 The spine region was utilized to obtain this profile. The boxes represent the noise level in the region thatthat should should represent represent smooth smooth signal signal intensity. intensity. The The gap gap of of signal signal intensity intensity between between the the highest highest and and the lowestthe lowest in box_a in box_a is larger is larger than thethan gap the of gap signal of signal intensity intensity in box_b. in box_b. In other In other words, words, it means it means that that box_a representedbox_a represented the mottled the imagemottled and image the and circles the represented circles represented the sharpness the sharpness of the edge,of the circle_bedge, circle_b showed theshowed definite the contrast definite as contrast compared as compared with circle_a, with and circle_a, moreover, and moreover, the edge information the edge information on the opposite on the of circle_aopposite was of distorted. circle_a was On distorted. the contrary, On thethe profilecontrary in, the Figure profile8b represents in Figure 8b symmetrical represents resultsymmetrical because theresult FNLM because denoising the FNLM algorithm denoising considers algorithm the geometrical considers composition the geometrical of the composition entire image of bythe using entire the Euclideanimage by distance. using the Euclidean distance.

Figure 8. The (a,b) are signal intensity profiles of the MASH phantom images applied the Wiener filter andFigure the FNLM 8. The denoising(a,b) are signal algorithm, intensity respectively. profiles of the The MASH graphs phantom represent images the signal applied intensity the Wiener of the yellowfilter linesand the in the FNLM images. denoising The boxes algorithm, represent respective the denoisingly. The graphs performance represent of thethe Wienersignal intensity filter and of the FNLM denoising algorithm. The circles represent the sharpness of the images.

Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 14

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 Appl.algorithm Sci. 2020 ,is10 ,more 7455 efficient than the conventional denoising filters for reducing the noise11 ofand 14 improving sharpness by measuring the signal intensity of each image.

Figure 9. (a,b) are signal intensity profiles of the 5-year-old phantom images applied the Wiener filter Figure 9. (a,b) are signal intensity profiles of the 5-year-old phantom images applied the Wiener filter and the FNLM denoising algorithm, respectively. The graphs represent the signal intensity of the 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 yellow lines in the images. The boxes represent the denoising performance of the Wiener filter and FNLM denoising algorithm. The circles represent the sharpness of the images. the FNLM denoising algorithm. The circles represent the sharpness of the images. Figure9 is the signal intensity profiles of the images that were obtained from the five-year-old phantom.In addition, The spine the region actual was computational utilized similar times to the were image measured of the MASH using phantom.a MATLAB The program boxes also to representcompare the time noise resolution level in the of regionthe FNLM that and should NLM represent denoising smooth algorithms. signal intensity.The actual In operation the profile time in Figurewas measured9b, the signal and intensity the average of box_b of is20 almost measurements flat and also was the calculated. contrast of circle_bAs a result, definitely the showaverage as comparedcomputational with thetime profile of the in FNLM Figure denoising9a. Therefore, algorithm we confirmed was 0.998 that s, thewhile FNLM that denoising of the NLM algorithm denoising is morealgorithm efficient was than 17.428 the conventionals. The time resolution denoising of filters the FNLM for reducing denoising the noise algorithm and improving was approximately sharpness by17.5× measuring better than the signal the conventional intensity of each algorithm image. due to a simplified computation of its weights. ObservingIn addition, Equation the actual (2), the computational X-axis () and times Y-axis were ( measured) components using aof MATLAB the image program are defined to compare in this theequation. time resolution In other words, of the the FNLM presence and NLMof two denoising axes necessitates algorithms. complicated The actual computations operation along time was two measureddimensions. and Therefore, the average as ofshown 20 measurements in Equation was(5), the calculated. size of the As matrix a result, was the reshaped average computational from (, ) to time(×,1 of the) because FNLM denoisingthe computer algorithm treats was(×,1 0.998) s,as whilea one-dimensional that of the NLM vector, denoising thus, simplifying algorithm was the 17.428computational s. The time complexity resolution [34,35]. of the FNLM Figure denoising 10 shows algorithm the time wasresolution approximately of the FNLM 17.5 better and NLM than × thealgorithms. conventional It can algorithm be observed due that to a the simplified proposed computation FNLM denoising of its weights.algorithm Observing significantly Equation improved (2), thethe X-axistime resolution (m) and Y-axis as compared (n) components with the ofconventional the image areNLM defined denoising in this algorithm. equation. In other words, the presenceIn this study, of two initially, axes necessitates we verified complicated that the noise computations level and along similarity two dimensions. of the thoracic Therefore, CT image as shownobtained in Equationfrom the (5),MASH the size phantom of the matrixare most was efficien reshapedtly improved from (m, n )by to the (m FNLMn, 1) because denoising the computeralgorithm × treatsas compared (m n, 1 )with as a one-dimensionalthe conventional vector,denoising thus, filters, simplifying and then the computationalwe applied the complexity FNLM denoising [34,35]. × Figurealgorithm 10 shows to the thepractical time resolutionthoracic CT of image the FNLM to demonstrate and NLM the algorithms. feasibility It of can the be proposed observed algorithm that the proposedin the clinical FNLM field. denoising In addition, algorithm we measured significantly the improved time resolution the time to resolution compare asthe compared FNLM and with NLM the conventionaldenoising algorithms. NLM denoising Thus, it algorithm. was demonstrated that computations could be effectively simplified by vectorization.In this study, initially, we verified that the noise level and similarity of the thoracic CT image obtainedConsequently, from the MASH we proposed phantom a aresolution most etoffi cientlyaddress improved the disadvantages by the FNLM of low-dose denoising examination algorithm asand compared conventional with denoising the conventional filters. Thus, denoising we expe filters,ct that and the then application we applied of thethe FNLMFNLM denoisingdenoising algorithm to the practical thoracic CT image to demonstrate the feasibility of the proposed algorithm in the clinical field. In addition, we measured the time resolution to compare the FNLM and NLM denoising algorithms. Thus, it was demonstrated that computations could be effectively simplified by vectorization. Consequently, we proposed a solution to address the disadvantages of low-dose examination and conventional denoising filters. Thus, we expect that the application of the FNLM denoising algorithm can contribute to the acquisition of high-quality images for the early diagnosis of lung cancer with as little exposure as possible. Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 14

Appl.algorithm Sci. 2020 can, 10, 7455contribute to the acquisition of high-quality images for the early diagnosis of12 lung of 14 cancer with as little exposure as possible.

FigureFigure 10. ComparisonComparison between between the the time time resolutions resolutions of the of theFNLM FNLM and andnon-local non-local means means (NLM) (NLM) denoisingdenoising algorithms.algorithms.

However,However, thethe results results reported reported in thisin this study study may ma varyy vary according according to some to conditionssome conditions of the utilized of the images.utilized Accordingimages. According to the study to the of Kornstudy et of al., Korn because et al., the because reconstruction the reconstruction algorithms algorithms affected the affected quality ofthe the quality image, of the the results image, reported the resu inlts this reported study coudin this be study affected coud when be affected the different when reconstruction the different algorithmsreconstruction were algorithms applied to were the image applied [36 ].to Then, the image the results [36]. Then, may vary the results depending may onvary whether depending artifacts on suchwhether as star-like artifacts artifact, such as beam star-like hardening artifact, artifact, beam hardening and ringing artifact, artifact, and are ringing present artifact, or not in are the present image. Becauseor not in the the artifactsimage. Because affect the the geometric artifacts structureaffect the ofgeometric image, the structure FNLM of denoising image, the algorithm FNLM denoising based on thealgorithm Euclidean based distance on the may Euclidean show varieddistance results. may show varied results. 5. Conclusions 5. Conclusions By comparing the images obtained with the FNLM denoising algorithm and other conventional By comparing the images obtained with the FNLM denoising algorithm and other conventional denoising filters, we demonstrated that the FNLM denoising algorithm achieved the best denoising denoising filters, we demonstrated that the FNLM denoising algorithm achieved the best denoising performance and similarity with the original image. In addition, we demonstrated that the performance and similarity with the original image. In addition, we demonstrated that the FNLM FNLM denoising algorithm improved the time resolution significantly as compared with the NLM denoising algorithm improved the time resolution significantly as compared with the NLM denoising algorithm. denoising algorithm. In conclusion, we expect that the FNLM denoising algorithm can contribute to reducing the ratio In conclusion, we expect that the FNLM denoising algorithm can contribute to reducing the ratio of misdiagnosis of thoracic disease and the exposure dose because the noise, which is the advantage of of misdiagnosis of thoracic disease and the exposure dose because the noise, which is the advantage the low-dose examination, can be suppressed efficiently by the FNLM denoising algorithm. Future of the low-dose examination, can be suppressed efficiently by the FNLM denoising algorithm. Future studies will focus on further improving the proposed algorithm to elicit better image characteristics. studies will focus on further improving the proposed algorithm to elicit better image characteristics.

AuthorAuthor Contributions:Contributions: Conceptualization, B.-G.K., H.-W.J., and Y.L.; DataData curation, B.-G.K., S.-H.K., and C.R.P.; Formal analysis, B.-G.K., S.-H.K., and Y.L.; Funding acquisition, H.-W.L.; Software, S.-H.K. and Y.L.; Formal analysis, B.-G.K., S.-H.K., and Y.L.; Funding acquisition, H.-W.L.; Software, S.-H.K. and Y.L.; Writing— Writing—original draft, B.-G.K., S.-H.K., and C.R.P.; Writing—review and editing, H.-W.L. and Y.L. All authors haveoriginal read draft, and B.-G.K., agreed to S.-H.K., the published and C.R.P.; version Writing—revi of the manuscript.ew and editing, H.-W.L. and Y.L. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the Technology Development Program (S2827843) funded by the Ministry ofFunding: SMEs and This Startups work (MSS,was supported Korea). by the Technology Development Program (S2827843) funded by the ConflictsMinistry of SMEs Interest: andThe Startups authors (MSS, declare Korea). no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest. References 1. Hricak, H.; Brenner, D.J.; Adelstein, S.J.; Frush, D.P.; Hall, E.J.; Howell, R.W.; McCollough, C.H.; Mettler, F.A.; Pearce, M.S.; Suleiman, O.H.; et al. Managing Radiation Use in Medical Imaging: A Multifaceted Challenge. Radiology 2011, 258, 889–905. [CrossRef][PubMed] 2. Shamsi, K.; Monfared, A.S.; Deevband, M.R.; Mohsenzadeh, B.; Ghorbani, M.; Gorji, K.E.; Niksirat, F. Evaluation of effective dose and entrance skin dose in digital radiology. Pol. J. Med. Phys. Eng. 2020, 26, 119–125. [CrossRef] Appl. Sci. 2020, 10, 7455 13 of 14

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