- Email: [email protected]
Total variation noise reduction algorithm in computed tomography image with custom-built phantom using 3D-printer
Radiation Physics and Chemistry 170 (2020) 108631
Contents lists available at ScienceDirect
Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Total variation noise reduction algorithm in computed tomography image with custom-built phantom using 3D-printer
T
Seong-Hyeon Kanga, Myeong-Seong Yoonb, Dong-Kyoon Hanb, Youngjin Leea,∗ a b
Department of Radiological Science, Gachon University, 191, Hambakmoero, Yeonsu-gu, Incheon, Republic of Korea Department of Radiological Science, 553, Sanseong-daero, Sujeong-gu, Gyeonggi-do, Eulji University, Republic of Korea
ARTICLE INFO
ABSTRACT
Keywords: Computed tomography Total variation Noise reduction algorithm 3D printer Image characteristic Quantitative evaluation
Noise in computed tomography (CT) is unavoidable because of various factors such as patient-source-related errors, hardware error, and electrical interference, which lead to unwanted diagnosis errors. Therefore, to solve this problem, we model a noise reduction algorithm based on total variation (TV) and applied it to images acquired using simulation study and 3D printing technology. Moreover, the conventional noise reduction algorithms are applied to the same image for comparative evaluation. For quantitative evaluation of the algorithms, we use the parameters of the coefficient of variation, signal-to-noise ratio, contrast-to-noise ratio, and normalized noise power spectrum. Our results indicate that the proposed TV noise reduction algorithm affords greater improvement in all the evaluation parameters considered in the simulation and 3D-printed phantom study, over the conventional noise reduction algorithms. In conclusion, we believe that our approach can significantly contribute to CT study and application.
1. Introduction Medical imaging with use of computed tomography (CT) based on X-rays has recently attracted increasing attention as an examination method that provides patient information without surgery (Moss et al., 1981). However, in CT, noise, which degrades the accuracy of image information, is produced owing to multiple factors in the process of image acquisition; these include patient-source-related errors, hardware errors, and electrical interference (Chen et al., 2018). To solve this problem, researchers have developed noise reduction algorithms such as the Gaussian filter, median filter, and Wiener filter, which are conventional techniques, by using software methods in image reconstruction processing (Wieneke, 2017). However, the abovementioned conventional noise reduction algorithms suffer form the degradation of the overall image characteristic because of the highfrequency signal loss in the reconstruction process despite the simplicity of both the equation for calculation and the method application to image (Kang et al., 2018). Contrastively, the total variation (TV) noise reduction algorithm can remove noise without high-frequency signal loss (Vishnukumar et al., 2017). The TV noise reduction algorithm reflects the interrelationship between the composition variate of the overall image after determination of the settings for a specific area based on the pixel value of the region of interest (ROI).
∗
In addition to noise, the image characteristic of a CT system is degraded by artifacts and blurring effects due to device deterioration or motion of the patient. These problems can be prevented with the application of certain quality control (QC) measures. In this case, QC involves the process of optimal device setting estimation and image acquisition of ensure accuracy. In particular, image accuracy is maintained via quantitative evaluations based on a device-exclusive phantom or human phantom (Lim et al., 2015; Choi et al., 2015). Thus, in this study, we designed and fabricated a phantom for the evaluation of the image characteristic using a three-dimensional (3D) printer. Presently, 3D printing technology can efficiently produce objects with complex internal structures based on designs specific to CT and magnetic resonance imaging (MRI) applications. Furthermore, a 3D printer can print the equivalent shape for each object during mass production. Accordingly, the use of 3D-printing technology in medical imaging has attracted considerable attention, with focus on developing surgical operation tools and phantoms for preprocessing (Muelleman et al., 2016; Cherkasskiy et al., 2017). Particularly, evaluated the image characteristic using 3D-printing technology and reconstruction algorithms (Solomon et al., 2014). Therefore, we attempted to evaluate efficacy of our proposed TV noise reduction algorithm using a 3Dprinted of our own design in this study.
Corresponding author. E-mail address: [email protected] (Y. Lee).
https://doi.org/10.1016/j.radphyschem.2019.108631 Received 11 June 2019; Received in revised form 17 October 2019; Accepted 29 November 2019 Available online 10 December 2019 0969-806X/ © 2019 Elsevier Ltd. All rights reserved.
Radiation Physics and Chemistry 170 (2020) 108631
S.-H. Kang, et al.
2. Materials and methods
2.2. Simulation study with Shepp–Logan phantom
2.1. Proposed TV noise reduction algorithm modeling
We acquired a Shepp-Logan phantom image with a size of 512 × 512 with Gaussian noise and a set standard deviation on 0.001 using the MATLAB software package. Next, the proposed TV noise reduction algorithm and conventional noise algorithms, namely, the Gaussian filter, median filter, and Wiener filter, were applied to the acquired image (Sundaram et al., 2014; Hoeher et al., 1997; Chen et al., 1987). Subsequently, the resulting images were analyzed and the efficacies of the various filters were comparatively evaluated.
A noise reduction algorithm is applied for the improvement of the image characteristic when an image is acquired using a digital radiography (DR) system. However, conventional noise reduction algorithms are associated with the problems of image characteristic degradation and signal loss of the included diagnostic information. Therefore, in this study, we designed a TV noise reduction algorithm based on the theory presented by Rudin et al. (1992). In general, a degradation image with white noise is modeled as follows (Seo et al., 2016):
2.3. Customized phantom study
(7)
g (x, y) = f (x , y ) + n (x , y )
We used a 3D printer based on the fused filament fabrication (FFF) technique (Ultimaker 3 Extended, Ultimaker, Netherlands) for fabricating our phantom, which was in the shape of the human skull (Fig. 1). The casing of the phantom was designed to be 16 cm, equal to the average diameter of a human skull, by use of SOLIDWORKS software. Further, we designed blocks that could be inserted into the casing of the phantom for simulation of the tissues inside the skull. The blocks were cylindrical in shape with a height of 6 cm and diameter of 5 cm. The blueprint data were converted into the STL format to achieve compatibility with the 3D printer. Subsequently, we formulated a G-code setting for the hardware and software of the 3D printer by using the QURA software package. Finally, the custom-built phantom casing was output using the 3D printer based on the generated G-code; here, we note that the material was composed of polylactic acid (PLA) filaments having a density similar to that of human tissue. In addition, the blocks were printed using various filaments, namely, acrylonitrile butadiene styrene (ABS), wood, and bronze filaments including XT-CF20, all of which afforded linear attenuation coefficients similar to those of the tissues inside the skull. Fig. 2 shows the printed phantom and CT image with the set ROIs and backgrounds for quantitative evaluation. The ROIs were set up with blocks of the custom-built phantom inserted to simulate tissue inside skull of human in a brain CT imaging environment. Labels a-e refer to the inserted materials consisting of XT-CF20, ABS, wood, bronze, and air, whereas labels 1–5 denote the corresponding backgrounds of the inserted materials. To acquire the phantom image, we used a 128-silce CT system (SOMATOM Definition AS+, Siemens Healthcare, Germany), and the system conditions were set as follows for the standard algorithms: tube current of 250 mAs under voltage of 80, 100, and 120 kVp for the
where represents the ideal image, n (x , y ) the electrical noise occurring during image acquisition, and g(x, y) the degraded image. Further, the gradient for the calculation of the difference between the ROI and neighborhood pixel value is defined as follows:
f (m , n)TV = =
M m=1
N n=1
M m=1
N n=1
(f (m , n )
f (m , n ) f (m
1, n))2 + (f (m , n)
f (m , n
1))2 (8)
where f (x , y ) M and N represent the numbers of rows and columns of image f (m , n) , respectively, and the gradient operator. In general, the l2 -norm is considered an effective operator to extract edges. However, the l2 -norm suffers from a high risk of false signal processing in terms of choosing noise signals over edge signals since it is very sensitive to noise. Therefore, we used the l1-norm as the gradient operator. Based on equation (8), we designed a TV noise reduction algorithm expressed as M
N
[f (m , n)|I (m , n)] =
f (m , n ) + m =1 n=1
2
I (m , n)
f (m , n ) 2
(9)
where denotes a control parameter that the two terms on the righthand side of the equation, and in this study, we set = 0.1. Further, M N f (m , n) can be used to determine the optimal solution. m=1 n=1
Further, 2 I (m , n) f (m , n) 2 represents the regulation fidelity term that indicates accuracy of the image information. Lastly, we used an adaptive average filter method, which applies the weighted value of the ROI and neighborhood pixel value through iterative utilization of equation (9).
Fig. 1. Construction of the 3D printer based on fused filament fabrication (FFF) technique and (b) 3D printer used in study.
2
Radiation Physics and Chemistry 170 (2020) 108631
S.-H. Kang, et al.
Fig. 2. (a) Printed custom-built phantom and (b) computed tomography (CT) image with set-up regions of interest (ROIs) and background for quantitative evaluation of CT image of phantom.
standard algorithms. Next, the CT images of the phantom were acquired 10 times with a fixed current of 250 mAs and varying voltages of 80, 100, and 120 kVp, respectively. In addition, image quantitative evaluation and analysis were performed after application of the conventional noise reduction algorithms and the proposed TV noise reduction algorithm.
terms of noise and signal on the reconstructed images which noise reduction algorithms applied. The MATLAB software (ver. 2015a. MATHWORKS, United States) package was used for the evaluation of the quantitative parameters.
COV =
2.4. Image characteristic evaluation
SNR =
We calculated coefficient of variation (COV), signal to noise ratio (SNR), contrast to noise ratio (CNR), and normalized noise power spectrum (NNPS) to compositely evaluate the image characteristics in
CNR =
A
(10)
µ
SA
(11)
A
SA 2 A
SB +
2 B
(12)
Fig. 3. Shepp-Logan images subjected to various algorithms for given region of interest (ROI) and background: (a) Original image (no algorithm applied), (b) Gaussian filtered, (c) median filtered, (d) Wiener filtered, and (e) total variation (TV) noise reduction filtered image. 3
Radiation Physics and Chemistry 170 (2020) 108631
S.-H. Kang, et al.
where SA and A represent the average signal intensity and standard deviation of the ROI, and SB and B the average signal intensity and standard deviation of the background region, respectively. Parameter NNPS analyzes the noise variation in the image over the spatial frequency range of interest.
NPS =
lim (Nx Ny x y ) < FTnk I (x , y )
Nx , Ny
(Nx Ny x y) M
=
lim
Nx , Ny, M
M m=1
x y M ·Nx Ny
NPSnormalized (u, v ) =
FTnk I (x , y )
M m=1
Nx i=1
Ny j=1
S (x , y )
S (x , y )
2
=
lim
Nx , Ny
3. Results 3.1. Results of simulation study with Shepp–Logan phantom We applied the conventional and proposed TV noise reduction algorithms to the Shepp-Logan phantom image with Gaussian noise in our simulation study. Fig. 3 shows the images acquired with the application of the conventional noise reduction algorithms and proposed TV noise reduction algorithms for the set-up ROIs and backgrounds. Fig. 4 depicts the calculated COV, SNR, and CNR values of the images after the application of the conventional noise reduction algorithms and proposed TV noise reduction algorithm. The calculated COV values of the original image and images after the application of the Gaussian filter, median filter, Wiener filter, and proposed TV noise reduction algorithm are approximately 0.35, 0.23, 0.14, 0.14, and 0.08 in the ROI, respectively. The calculated SNR values of the original image and the images after the application of the Gaussian filter, median filter, Wiener filter, and proposed TV noise reduction algorithm are approximately 0.67, 1.05, 0.64, 2.04, and 6.71 in the ROI, respectively. Further, the calculated CNR values of the original image and the images
lim
M
2 2
(I (x i , yj )
NPS (u, v ) (large area signal) 2
S (x i , yj )) e
2 i(un xi + vk yi )
(13)
where I (x , y ) denotes the average image intensity, S (x , y ) the average background intensity, Nx , Ny the pixel numbers along the X- and Y-axis, and x , y the pixel sizes along the X- and Y-axis, respectively.
Fig. 4. Coefficient of variation (COV), signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) of regions of interest (ROIs) in computed tomography (CT) images of Shepp-Logan phantom.
4
Radiation Physics and Chemistry 170 (2020) 108631
S.-H. Kang, et al.
3.2. Results of custom-built phantom study Fig. 6 presents the CT images of the custom-built phantom obtained after application of the noise reduction algorithms under varying applied voltages of 80, 100, and 120 kVp at a current of 250 mAs. In addition, we calculated the quantitative evaluation parameters for analysis of the effectiveness of the proposed TV noise reduction algorithm based 10 CT images. Fig. 7 shows the COV calculated from the CT images obtained with application of the noise reduction algorithms to each material used in the phantom. The calculated average COV values of the original image and those of the images obtained after the application of the Gaussian filter, median filter, Wiener filter, and proposed TV noise reduction algorithm are approximately 0.065, 0.049, 0.040, 0.038, and 0.030, respectively, for the total material at 80 kVp. In addition, the COV values are on average approximately 0.060, 0.043, 0.033, 0.030, and 0.022 at 100 kVp, respectively. Moreover, these average COV values are approximately 0.057, 0.042, 0.031, 0.029, and 0.020 at 120 kVp, respectively. The calculated SNR values of the original image and images acquired after the application of the Gaussian filter, median filter, Wiener filter, and proposed TV noise reduction algorithm are on average approximately 21.99, 32.37, 48.77, 54.75, and 98.33 in all the materials at 80 kVp, respectively (Fig. 8). In addition, the SNR values are on average approximately 21.38, 30.88, 43.40, 49.13, and 77.05 at 100 kVp, respectively. Moreover, the SNR values are on average approximately 21.76, 31.84, 45.96, 52.60, and 87.45 at 120 kVp, respectively. Fig. 9 shows the CNR values calculated from the CT images obtained with the application of the noise reduction algorithms to each material. The calculated CNR values of the original image and the images after
Fig. 5. Normalized noise power spectrum (NNPS) results for computed tomography (CT) image of Shepp-Logan phantom.
after the application of the Gaussian filter, median filter, Wiener filter, and proposed TV noise reduction algorithm are approximately 4.25, 6.61, 11.57, 11.34, and 20.19 in the ROI, respectively. Fig. 5 shows the NNPS results of the images after the application of the conventional noise reduction algorithms and proposed TV noise reduction algorithm. In the original image, the NNPS is distributed regularly over 10 2 mm2 in the spatial frequency range of 1–4 lp/mm. With the application of the noise reduction algorithms, there is a gradual decrease in the noise relative to that in the original image with increase in the spatial frequency.
Fig. 6. Computed tomography (CT) images of custom-built phantom obtained using noise reduction algorithms under voltages of (a) 80, (b) 100, and (c) 120 kVp at tube current of 250 mAs.
5
Radiation Physics and Chemistry 170 (2020) 108631
S.-H. Kang, et al.
Fig. 7. Coefficient of variation (COV) for given regions of interest (ROIs) in computed tomography (CT) images of custom-built phantom under voltages of (a) 80, (b) 100, and (c) 120 kVp.
the application of the Gaussian filter, median filter, Wiener filter, and proposed TV noise reduction algorithm are on average approximately 14.80, 19.22, 23.84, 25.39, and 34.02 in all the materials at 80 kVp, respectively. In addition, these CNR values are on average approximately 16.62, 22.77, 29.48, 32.66, and 49.33 at 100 kVp, respectively. Moreover, these CNR values are on average approximately 17.13, 24.09, 31.71, 35.34, and 54.46 at 120 kVp, respectively. Fig. 10 shows the NNPS results of the images after application of the conventional noise reduction algorithms and proposed TV noise reduction algorithm. In all the images, the NNPS values gradually decreases with increase in the spatial frequency. With the application of the proposed TV noise reduction algorithm, the gradual decrease in the NNPS is approximately 10 2 mm2 compared with that of the original image with increase in the spatial frequency.
However, CT systems suffer from problems such as device degradation, performance decline of the detector, and patient motion during CT, which can lead to misdiagnosis. In such a case, the faulty image is rejected, and subsequently, there is increased exposure of the patient to radiation. Therefore, the resulting generated noise can cause errors in the information transmission process since the noise is sensitive to the radiation dose. To resolve this problem, various methods have been suggested in many studies. In particular, algorithms were developed using software programs and applies in image processing. However, conventional noise reduction algorithms suffer from the limitations of deterioration of the image characteristic and efficiency. Therefore, in this study, we proposed a noise reduction algorithm based on TV. The TV algorithm is known to exhibit high noise reduction (Kim et al., 2018), and it has been applied in MRI and ultrasound imaging systems as well as X-ray systems (Block et al., 2007). Based on these existing studies, we modeled our proposed TV noise reduction algorithm. Meanwhile, various studies have focused on the use of 3D printing in medical imaging. In particular, studies have been conducted to improve the accuracy of the image acquisition procedure and its robustness to
4. Discussion X-ray-based CT systems are widely used for non-invasive medical imaging to carry out patient diagnosis in the field of radiology.
6
Radiation Physics and Chemistry 170 (2020) 108631
S.-H. Kang, et al.
Fig. 8. Signal-to-noise ratios (SNRs) of regions of interest (ROIs) in computed tomography (CT) images of custom-built phantom under voltages of (a) 80, (b) 100, and (c) 120 kVp.
unexpected conditions using 3D printing technology based on 3D medical images (Chan et al., 2015). However, studies on the printing of phantoms for the evaluation of the image characteristic have attracted relatively little interest. Therefore, in the study, we also constructed a phantom to evaluate the image characteristic and attempted to study the usefulness of the phantom in imaging. To prove the efficacy of the proposed TV noise reduction algorithm, we evaluated it against conventional noise reduction algorithms. In addition, we fabricated a phantom simulating a human skull using 3D printing technology. The custom-designed phantom was printed on a 16 cm diameter filament composed of a material having a density similar to that of human brain tissue. Next, we analyzed the efficiency of the proposed TV noise reduction algorithm via comparative evaluation with conventional noise reduction algorithms, namely, the Gaussian filter, median filter, and Wiener filter algorithms. Subsequently, we used parameters relevant to noise, e.g., COV, SNR, CNR, and NNPS, to evaluate the algorithm efficiencies. As per the results of the simulation study, the COV, SNR, and CNR of the proposed TV noise reduction algorithm exhibited improvements by
factors of approximately 4.32, 9.99, and 4.75 relative to the corresponding ones, respectively, of the original image. In addition, the NNPS of the proposed TV noise reduction algorithm was improved by a factor about 10 2 mm2 over that of the original image. In the customized phantom study, the quantitative factors were evaluated with the use of the filament materials of XT-CT20, ABS, wood, bronze, and air. Consequently, the COV of the image after the application of the proposed TV noise reduction algorithm showed an improvement by approximately 3.05, 1.63, 2.15, and 1.57 times the COV values of the original image and images acquired after application of the Gaussian filter, median filter, and Wiener filter for all the materials, respectively. The SNR of the image denoised with the proposed TV noise reduction algorithm showed improvements of approximately 4.42, 2.06, 2.95, and 1.99 times that of the original image and images acquired after the application of the Gaussian filter, median filter, and Wiener filter for all the materials, respectively. The CNR of the image subjected to the proposed TV noise reduction algorithm showed improvement by factors of approximately 4.85, 2.30, 3.24, and 2.04 over the CNR values of the original image and images subjected to the Gaussian filter, median
7
Radiation Physics and Chemistry 170 (2020) 108631
S.-H. Kang, et al.
Fig. 9. Contrast-to-noise ratio (CNRs) of regions of interest (ROIs) in computed tomography (CT) images of custom-built phantom under voltages of (a) 80, (b) 100, and (c) 120 kVp.
filter, and Wiener filter for all the materials, respectively. In addition, the NNPS of the image subjected to the proposed TV noise reduction algorithm was improved by approximately 10 2 mm2 over that of the original image. Many studies on TV noise reduction algorithms have been conducted in order to improve the image characteristic. Previously, the TV noise reduction algorithm formula including the gradient operator, control parameter, regularization formula, and fidelity term similar to our proposed TV noise reduction algorithm has been modeled by Rudin et al. (1992). According to their results, the TV noise reduction algorithm is effective for reducing Gaussian noise, and it can improve the SNR of 2D image. In our study, we also fabricated a human phantom composed of filaments of various materials using a 3D printer. The materials were used to simulate human tissues to obtain accurate results. One of the major advantages of our algorithm is that it can improve the image characteristic without signal loss while affording noise reduction. Subsequently, we quantitatively evaluated the proposed TV noise reduction algorithm using parameters COV, SNR, CNR, and NNPS
that can reflect both the noise and image characteristic. Our results demonstrated that the proposed TV noise reduction algorithm can remove noise while simultaneously affording improvements in the image characteristic. 5. Conclusions In this study, we proposed and modeled a TV noise reduction algorithm for denoising medical images acquired from CT systems. A customized phantom was printed using a 3D printer to evaluate the image characteristic. In addition, we performed a comparative evaluation of our algorithm with conventional noise reduction algorithms to demonstrate the efficacy of the proposed TV noise reduction algorithm. In both the simulation and phantom study, all the quantitative evaluation factors showed improvements in the proposed TV noise reduction over the conventional noise reduction algorithms. Therefore, we believe that the proposed TV noise reduction algorithm can replace
8
Radiation Physics and Chemistry 170 (2020) 108631
S.-H. Kang, et al.
Fig. 10. Normalized noise power spectrum (NNPS) results of regions of interest (ROIs) in computed tomography (CT) images of custom-built phantom applied voltages of (a) 80, (b) 100, and (c) 120 kVp, respectively.
conventional noise reduction algorithms. Moreover, based on the results of this study, we plan to apply proposed TV noise reduction algorithm for the custom-built phantom using 3D printing technology in various medical imaging system.
References Block, K.T., et al., 2007. Magnetic resonance in medicine. Off. J. Int. Soc. Magn. Reson. Med. 57, 1086. Chan, H.H., et al., 2015. PLoS One 10. https://doi.org/10.1371/journal.pone.0136370. Chen, W., et al., 2018. IEEE Access 6, 78892. Chen, J.S., et al., 1987. IEEE Trans. Pattern Anal. Mach. Intell. 4, 584. Cherkasskiy, L., et al., 2017. J. Child. Orthopaed. 11, 147. Choi, S.Y., et al., 2015. Br. Inst. Radiol. 89, 1058. Hoeher, P., et al., 1997. In: IEEE International Conference on Acoustics, Speech, and Signal Processing 3. pp. 1845. Kang, S.H., et al., 2018. Optik 156, 197. Kim, D., et al., 2018. Optik 161, 270. Lim, K., et al., 2015. J. Comput. Assist. Tomogr. 39, 443. Moss, A.A., et al., 1981. Gastroenterology 80, 45. Muelleman, T.J., et al., 2016. J. Neurol. Surg. Part B Skull Base 77, 243. Rudin, L.I., et al., 1992. Physica D 60, 259. Seo, K., et al., 2016. J. Magn. 21, 593. Solomon, J., et al., 2014. Medical imaging 2014. Phys. Med. Imag. https://doi.org/10. 1117/12.2043555. Sundaram, K., et al., 2014. Int. J. Innov. Res. Sci. Eng. Technol. 3, 10333. Vishnukumar, S., et al., 2017. Opt. Commun. 404, 80. Wieneke, B., 2017. Exp. Fluid 58, 94.
Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This research was supported by the National Research Foundation of Korea (NRF-2016R1D1A1B03930357) and (NRF2019R1F1A1062811). Dong-Kyoon Han and Youngjin Lee contributed equally to the writing of this paper.
9
Contents lists available at ScienceDirect
Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Total variation noise reduction algorithm in computed tomography image with custom-built phantom using 3D-printer
T
Seong-Hyeon Kanga, Myeong-Seong Yoonb, Dong-Kyoon Hanb, Youngjin Leea,∗ a b
Department of Radiological Science, Gachon University, 191, Hambakmoero, Yeonsu-gu, Incheon, Republic of Korea Department of Radiological Science, 553, Sanseong-daero, Sujeong-gu, Gyeonggi-do, Eulji University, Republic of Korea
ARTICLE INFO
ABSTRACT
Keywords: Computed tomography Total variation Noise reduction algorithm 3D printer Image characteristic Quantitative evaluation
Noise in computed tomography (CT) is unavoidable because of various factors such as patient-source-related errors, hardware error, and electrical interference, which lead to unwanted diagnosis errors. Therefore, to solve this problem, we model a noise reduction algorithm based on total variation (TV) and applied it to images acquired using simulation study and 3D printing technology. Moreover, the conventional noise reduction algorithms are applied to the same image for comparative evaluation. For quantitative evaluation of the algorithms, we use the parameters of the coefficient of variation, signal-to-noise ratio, contrast-to-noise ratio, and normalized noise power spectrum. Our results indicate that the proposed TV noise reduction algorithm affords greater improvement in all the evaluation parameters considered in the simulation and 3D-printed phantom study, over the conventional noise reduction algorithms. In conclusion, we believe that our approach can significantly contribute to CT study and application.
1. Introduction Medical imaging with use of computed tomography (CT) based on X-rays has recently attracted increasing attention as an examination method that provides patient information without surgery (Moss et al., 1981). However, in CT, noise, which degrades the accuracy of image information, is produced owing to multiple factors in the process of image acquisition; these include patient-source-related errors, hardware errors, and electrical interference (Chen et al., 2018). To solve this problem, researchers have developed noise reduction algorithms such as the Gaussian filter, median filter, and Wiener filter, which are conventional techniques, by using software methods in image reconstruction processing (Wieneke, 2017). However, the abovementioned conventional noise reduction algorithms suffer form the degradation of the overall image characteristic because of the highfrequency signal loss in the reconstruction process despite the simplicity of both the equation for calculation and the method application to image (Kang et al., 2018). Contrastively, the total variation (TV) noise reduction algorithm can remove noise without high-frequency signal loss (Vishnukumar et al., 2017). The TV noise reduction algorithm reflects the interrelationship between the composition variate of the overall image after determination of the settings for a specific area based on the pixel value of the region of interest (ROI).
∗
In addition to noise, the image characteristic of a CT system is degraded by artifacts and blurring effects due to device deterioration or motion of the patient. These problems can be prevented with the application of certain quality control (QC) measures. In this case, QC involves the process of optimal device setting estimation and image acquisition of ensure accuracy. In particular, image accuracy is maintained via quantitative evaluations based on a device-exclusive phantom or human phantom (Lim et al., 2015; Choi et al., 2015). Thus, in this study, we designed and fabricated a phantom for the evaluation of the image characteristic using a three-dimensional (3D) printer. Presently, 3D printing technology can efficiently produce objects with complex internal structures based on designs specific to CT and magnetic resonance imaging (MRI) applications. Furthermore, a 3D printer can print the equivalent shape for each object during mass production. Accordingly, the use of 3D-printing technology in medical imaging has attracted considerable attention, with focus on developing surgical operation tools and phantoms for preprocessing (Muelleman et al., 2016; Cherkasskiy et al., 2017). Particularly, evaluated the image characteristic using 3D-printing technology and reconstruction algorithms (Solomon et al., 2014). Therefore, we attempted to evaluate efficacy of our proposed TV noise reduction algorithm using a 3Dprinted of our own design in this study.
Corresponding author. E-mail address: [email protected] (Y. Lee).
https://doi.org/10.1016/j.radphyschem.2019.108631 Received 11 June 2019; Received in revised form 17 October 2019; Accepted 29 November 2019 Available online 10 December 2019 0969-806X/ © 2019 Elsevier Ltd. All rights reserved.
Radiation Physics and Chemistry 170 (2020) 108631
S.-H. Kang, et al.
2. Materials and methods
2.2. Simulation study with Shepp–Logan phantom
2.1. Proposed TV noise reduction algorithm modeling
We acquired a Shepp-Logan phantom image with a size of 512 × 512 with Gaussian noise and a set standard deviation on 0.001 using the MATLAB software package. Next, the proposed TV noise reduction algorithm and conventional noise algorithms, namely, the Gaussian filter, median filter, and Wiener filter, were applied to the acquired image (Sundaram et al., 2014; Hoeher et al., 1997; Chen et al., 1987). Subsequently, the resulting images were analyzed and the efficacies of the various filters were comparatively evaluated.
A noise reduction algorithm is applied for the improvement of the image characteristic when an image is acquired using a digital radiography (DR) system. However, conventional noise reduction algorithms are associated with the problems of image characteristic degradation and signal loss of the included diagnostic information. Therefore, in this study, we designed a TV noise reduction algorithm based on the theory presented by Rudin et al. (1992). In general, a degradation image with white noise is modeled as follows (Seo et al., 2016):
2.3. Customized phantom study
(7)
g (x, y) = f (x , y ) + n (x , y )
We used a 3D printer based on the fused filament fabrication (FFF) technique (Ultimaker 3 Extended, Ultimaker, Netherlands) for fabricating our phantom, which was in the shape of the human skull (Fig. 1). The casing of the phantom was designed to be 16 cm, equal to the average diameter of a human skull, by use of SOLIDWORKS software. Further, we designed blocks that could be inserted into the casing of the phantom for simulation of the tissues inside the skull. The blocks were cylindrical in shape with a height of 6 cm and diameter of 5 cm. The blueprint data were converted into the STL format to achieve compatibility with the 3D printer. Subsequently, we formulated a G-code setting for the hardware and software of the 3D printer by using the QURA software package. Finally, the custom-built phantom casing was output using the 3D printer based on the generated G-code; here, we note that the material was composed of polylactic acid (PLA) filaments having a density similar to that of human tissue. In addition, the blocks were printed using various filaments, namely, acrylonitrile butadiene styrene (ABS), wood, and bronze filaments including XT-CF20, all of which afforded linear attenuation coefficients similar to those of the tissues inside the skull. Fig. 2 shows the printed phantom and CT image with the set ROIs and backgrounds for quantitative evaluation. The ROIs were set up with blocks of the custom-built phantom inserted to simulate tissue inside skull of human in a brain CT imaging environment. Labels a-e refer to the inserted materials consisting of XT-CF20, ABS, wood, bronze, and air, whereas labels 1–5 denote the corresponding backgrounds of the inserted materials. To acquire the phantom image, we used a 128-silce CT system (SOMATOM Definition AS+, Siemens Healthcare, Germany), and the system conditions were set as follows for the standard algorithms: tube current of 250 mAs under voltage of 80, 100, and 120 kVp for the
where represents the ideal image, n (x , y ) the electrical noise occurring during image acquisition, and g(x, y) the degraded image. Further, the gradient for the calculation of the difference between the ROI and neighborhood pixel value is defined as follows:
f (m , n)TV = =
M m=1
N n=1
M m=1
N n=1
(f (m , n )
f (m , n ) f (m
1, n))2 + (f (m , n)
f (m , n
1))2 (8)
where f (x , y ) M and N represent the numbers of rows and columns of image f (m , n) , respectively, and the gradient operator. In general, the l2 -norm is considered an effective operator to extract edges. However, the l2 -norm suffers from a high risk of false signal processing in terms of choosing noise signals over edge signals since it is very sensitive to noise. Therefore, we used the l1-norm as the gradient operator. Based on equation (8), we designed a TV noise reduction algorithm expressed as M
N
[f (m , n)|I (m , n)] =
f (m , n ) + m =1 n=1
2
I (m , n)
f (m , n ) 2
(9)
where denotes a control parameter that the two terms on the righthand side of the equation, and in this study, we set = 0.1. Further, M N f (m , n) can be used to determine the optimal solution. m=1 n=1
Further, 2 I (m , n) f (m , n) 2 represents the regulation fidelity term that indicates accuracy of the image information. Lastly, we used an adaptive average filter method, which applies the weighted value of the ROI and neighborhood pixel value through iterative utilization of equation (9).
Fig. 1. Construction of the 3D printer based on fused filament fabrication (FFF) technique and (b) 3D printer used in study.
2
Radiation Physics and Chemistry 170 (2020) 108631
S.-H. Kang, et al.
Fig. 2. (a) Printed custom-built phantom and (b) computed tomography (CT) image with set-up regions of interest (ROIs) and background for quantitative evaluation of CT image of phantom.
standard algorithms. Next, the CT images of the phantom were acquired 10 times with a fixed current of 250 mAs and varying voltages of 80, 100, and 120 kVp, respectively. In addition, image quantitative evaluation and analysis were performed after application of the conventional noise reduction algorithms and the proposed TV noise reduction algorithm.
terms of noise and signal on the reconstructed images which noise reduction algorithms applied. The MATLAB software (ver. 2015a. MATHWORKS, United States) package was used for the evaluation of the quantitative parameters.
COV =
2.4. Image characteristic evaluation
SNR =
We calculated coefficient of variation (COV), signal to noise ratio (SNR), contrast to noise ratio (CNR), and normalized noise power spectrum (NNPS) to compositely evaluate the image characteristics in
CNR =
A
(10)
µ
SA
(11)
A
SA 2 A
SB +
2 B
(12)
Fig. 3. Shepp-Logan images subjected to various algorithms for given region of interest (ROI) and background: (a) Original image (no algorithm applied), (b) Gaussian filtered, (c) median filtered, (d) Wiener filtered, and (e) total variation (TV) noise reduction filtered image. 3
Radiation Physics and Chemistry 170 (2020) 108631
S.-H. Kang, et al.
where SA and A represent the average signal intensity and standard deviation of the ROI, and SB and B the average signal intensity and standard deviation of the background region, respectively. Parameter NNPS analyzes the noise variation in the image over the spatial frequency range of interest.
NPS =
lim (Nx Ny x y ) < FTnk I (x , y )
Nx , Ny
(Nx Ny x y) M
=
lim
Nx , Ny, M
M m=1
x y M ·Nx Ny
NPSnormalized (u, v ) =
FTnk I (x , y )
M m=1
Nx i=1
Ny j=1
S (x , y )
S (x , y )
2
=
lim
Nx , Ny
3. Results 3.1. Results of simulation study with Shepp–Logan phantom We applied the conventional and proposed TV noise reduction algorithms to the Shepp-Logan phantom image with Gaussian noise in our simulation study. Fig. 3 shows the images acquired with the application of the conventional noise reduction algorithms and proposed TV noise reduction algorithms for the set-up ROIs and backgrounds. Fig. 4 depicts the calculated COV, SNR, and CNR values of the images after the application of the conventional noise reduction algorithms and proposed TV noise reduction algorithm. The calculated COV values of the original image and images after the application of the Gaussian filter, median filter, Wiener filter, and proposed TV noise reduction algorithm are approximately 0.35, 0.23, 0.14, 0.14, and 0.08 in the ROI, respectively. The calculated SNR values of the original image and the images after the application of the Gaussian filter, median filter, Wiener filter, and proposed TV noise reduction algorithm are approximately 0.67, 1.05, 0.64, 2.04, and 6.71 in the ROI, respectively. Further, the calculated CNR values of the original image and the images
lim
M
2 2
(I (x i , yj )
NPS (u, v ) (large area signal) 2
S (x i , yj )) e
2 i(un xi + vk yi )
(13)
where I (x , y ) denotes the average image intensity, S (x , y ) the average background intensity, Nx , Ny the pixel numbers along the X- and Y-axis, and x , y the pixel sizes along the X- and Y-axis, respectively.
Fig. 4. Coefficient of variation (COV), signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) of regions of interest (ROIs) in computed tomography (CT) images of Shepp-Logan phantom.
4
Radiation Physics and Chemistry 170 (2020) 108631
S.-H. Kang, et al.
3.2. Results of custom-built phantom study Fig. 6 presents the CT images of the custom-built phantom obtained after application of the noise reduction algorithms under varying applied voltages of 80, 100, and 120 kVp at a current of 250 mAs. In addition, we calculated the quantitative evaluation parameters for analysis of the effectiveness of the proposed TV noise reduction algorithm based 10 CT images. Fig. 7 shows the COV calculated from the CT images obtained with application of the noise reduction algorithms to each material used in the phantom. The calculated average COV values of the original image and those of the images obtained after the application of the Gaussian filter, median filter, Wiener filter, and proposed TV noise reduction algorithm are approximately 0.065, 0.049, 0.040, 0.038, and 0.030, respectively, for the total material at 80 kVp. In addition, the COV values are on average approximately 0.060, 0.043, 0.033, 0.030, and 0.022 at 100 kVp, respectively. Moreover, these average COV values are approximately 0.057, 0.042, 0.031, 0.029, and 0.020 at 120 kVp, respectively. The calculated SNR values of the original image and images acquired after the application of the Gaussian filter, median filter, Wiener filter, and proposed TV noise reduction algorithm are on average approximately 21.99, 32.37, 48.77, 54.75, and 98.33 in all the materials at 80 kVp, respectively (Fig. 8). In addition, the SNR values are on average approximately 21.38, 30.88, 43.40, 49.13, and 77.05 at 100 kVp, respectively. Moreover, the SNR values are on average approximately 21.76, 31.84, 45.96, 52.60, and 87.45 at 120 kVp, respectively. Fig. 9 shows the CNR values calculated from the CT images obtained with the application of the noise reduction algorithms to each material. The calculated CNR values of the original image and the images after
Fig. 5. Normalized noise power spectrum (NNPS) results for computed tomography (CT) image of Shepp-Logan phantom.
after the application of the Gaussian filter, median filter, Wiener filter, and proposed TV noise reduction algorithm are approximately 4.25, 6.61, 11.57, 11.34, and 20.19 in the ROI, respectively. Fig. 5 shows the NNPS results of the images after the application of the conventional noise reduction algorithms and proposed TV noise reduction algorithm. In the original image, the NNPS is distributed regularly over 10 2 mm2 in the spatial frequency range of 1–4 lp/mm. With the application of the noise reduction algorithms, there is a gradual decrease in the noise relative to that in the original image with increase in the spatial frequency.
Fig. 6. Computed tomography (CT) images of custom-built phantom obtained using noise reduction algorithms under voltages of (a) 80, (b) 100, and (c) 120 kVp at tube current of 250 mAs.
5
Radiation Physics and Chemistry 170 (2020) 108631
S.-H. Kang, et al.
Fig. 7. Coefficient of variation (COV) for given regions of interest (ROIs) in computed tomography (CT) images of custom-built phantom under voltages of (a) 80, (b) 100, and (c) 120 kVp.
the application of the Gaussian filter, median filter, Wiener filter, and proposed TV noise reduction algorithm are on average approximately 14.80, 19.22, 23.84, 25.39, and 34.02 in all the materials at 80 kVp, respectively. In addition, these CNR values are on average approximately 16.62, 22.77, 29.48, 32.66, and 49.33 at 100 kVp, respectively. Moreover, these CNR values are on average approximately 17.13, 24.09, 31.71, 35.34, and 54.46 at 120 kVp, respectively. Fig. 10 shows the NNPS results of the images after application of the conventional noise reduction algorithms and proposed TV noise reduction algorithm. In all the images, the NNPS values gradually decreases with increase in the spatial frequency. With the application of the proposed TV noise reduction algorithm, the gradual decrease in the NNPS is approximately 10 2 mm2 compared with that of the original image with increase in the spatial frequency.
However, CT systems suffer from problems such as device degradation, performance decline of the detector, and patient motion during CT, which can lead to misdiagnosis. In such a case, the faulty image is rejected, and subsequently, there is increased exposure of the patient to radiation. Therefore, the resulting generated noise can cause errors in the information transmission process since the noise is sensitive to the radiation dose. To resolve this problem, various methods have been suggested in many studies. In particular, algorithms were developed using software programs and applies in image processing. However, conventional noise reduction algorithms suffer from the limitations of deterioration of the image characteristic and efficiency. Therefore, in this study, we proposed a noise reduction algorithm based on TV. The TV algorithm is known to exhibit high noise reduction (Kim et al., 2018), and it has been applied in MRI and ultrasound imaging systems as well as X-ray systems (Block et al., 2007). Based on these existing studies, we modeled our proposed TV noise reduction algorithm. Meanwhile, various studies have focused on the use of 3D printing in medical imaging. In particular, studies have been conducted to improve the accuracy of the image acquisition procedure and its robustness to
4. Discussion X-ray-based CT systems are widely used for non-invasive medical imaging to carry out patient diagnosis in the field of radiology.
6
Radiation Physics and Chemistry 170 (2020) 108631
S.-H. Kang, et al.
Fig. 8. Signal-to-noise ratios (SNRs) of regions of interest (ROIs) in computed tomography (CT) images of custom-built phantom under voltages of (a) 80, (b) 100, and (c) 120 kVp.
unexpected conditions using 3D printing technology based on 3D medical images (Chan et al., 2015). However, studies on the printing of phantoms for the evaluation of the image characteristic have attracted relatively little interest. Therefore, in the study, we also constructed a phantom to evaluate the image characteristic and attempted to study the usefulness of the phantom in imaging. To prove the efficacy of the proposed TV noise reduction algorithm, we evaluated it against conventional noise reduction algorithms. In addition, we fabricated a phantom simulating a human skull using 3D printing technology. The custom-designed phantom was printed on a 16 cm diameter filament composed of a material having a density similar to that of human brain tissue. Next, we analyzed the efficiency of the proposed TV noise reduction algorithm via comparative evaluation with conventional noise reduction algorithms, namely, the Gaussian filter, median filter, and Wiener filter algorithms. Subsequently, we used parameters relevant to noise, e.g., COV, SNR, CNR, and NNPS, to evaluate the algorithm efficiencies. As per the results of the simulation study, the COV, SNR, and CNR of the proposed TV noise reduction algorithm exhibited improvements by
factors of approximately 4.32, 9.99, and 4.75 relative to the corresponding ones, respectively, of the original image. In addition, the NNPS of the proposed TV noise reduction algorithm was improved by a factor about 10 2 mm2 over that of the original image. In the customized phantom study, the quantitative factors were evaluated with the use of the filament materials of XT-CT20, ABS, wood, bronze, and air. Consequently, the COV of the image after the application of the proposed TV noise reduction algorithm showed an improvement by approximately 3.05, 1.63, 2.15, and 1.57 times the COV values of the original image and images acquired after application of the Gaussian filter, median filter, and Wiener filter for all the materials, respectively. The SNR of the image denoised with the proposed TV noise reduction algorithm showed improvements of approximately 4.42, 2.06, 2.95, and 1.99 times that of the original image and images acquired after the application of the Gaussian filter, median filter, and Wiener filter for all the materials, respectively. The CNR of the image subjected to the proposed TV noise reduction algorithm showed improvement by factors of approximately 4.85, 2.30, 3.24, and 2.04 over the CNR values of the original image and images subjected to the Gaussian filter, median
7
Radiation Physics and Chemistry 170 (2020) 108631
S.-H. Kang, et al.
Fig. 9. Contrast-to-noise ratio (CNRs) of regions of interest (ROIs) in computed tomography (CT) images of custom-built phantom under voltages of (a) 80, (b) 100, and (c) 120 kVp.
filter, and Wiener filter for all the materials, respectively. In addition, the NNPS of the image subjected to the proposed TV noise reduction algorithm was improved by approximately 10 2 mm2 over that of the original image. Many studies on TV noise reduction algorithms have been conducted in order to improve the image characteristic. Previously, the TV noise reduction algorithm formula including the gradient operator, control parameter, regularization formula, and fidelity term similar to our proposed TV noise reduction algorithm has been modeled by Rudin et al. (1992). According to their results, the TV noise reduction algorithm is effective for reducing Gaussian noise, and it can improve the SNR of 2D image. In our study, we also fabricated a human phantom composed of filaments of various materials using a 3D printer. The materials were used to simulate human tissues to obtain accurate results. One of the major advantages of our algorithm is that it can improve the image characteristic without signal loss while affording noise reduction. Subsequently, we quantitatively evaluated the proposed TV noise reduction algorithm using parameters COV, SNR, CNR, and NNPS
that can reflect both the noise and image characteristic. Our results demonstrated that the proposed TV noise reduction algorithm can remove noise while simultaneously affording improvements in the image characteristic. 5. Conclusions In this study, we proposed and modeled a TV noise reduction algorithm for denoising medical images acquired from CT systems. A customized phantom was printed using a 3D printer to evaluate the image characteristic. In addition, we performed a comparative evaluation of our algorithm with conventional noise reduction algorithms to demonstrate the efficacy of the proposed TV noise reduction algorithm. In both the simulation and phantom study, all the quantitative evaluation factors showed improvements in the proposed TV noise reduction over the conventional noise reduction algorithms. Therefore, we believe that the proposed TV noise reduction algorithm can replace
8
Radiation Physics and Chemistry 170 (2020) 108631
S.-H. Kang, et al.
Fig. 10. Normalized noise power spectrum (NNPS) results of regions of interest (ROIs) in computed tomography (CT) images of custom-built phantom applied voltages of (a) 80, (b) 100, and (c) 120 kVp, respectively.
conventional noise reduction algorithms. Moreover, based on the results of this study, we plan to apply proposed TV noise reduction algorithm for the custom-built phantom using 3D printing technology in various medical imaging system.
References Block, K.T., et al., 2007. Magnetic resonance in medicine. Off. J. Int. Soc. Magn. Reson. Med. 57, 1086. Chan, H.H., et al., 2015. PLoS One 10. https://doi.org/10.1371/journal.pone.0136370. Chen, W., et al., 2018. IEEE Access 6, 78892. Chen, J.S., et al., 1987. IEEE Trans. Pattern Anal. Mach. Intell. 4, 584. Cherkasskiy, L., et al., 2017. J. Child. Orthopaed. 11, 147. Choi, S.Y., et al., 2015. Br. Inst. Radiol. 89, 1058. Hoeher, P., et al., 1997. In: IEEE International Conference on Acoustics, Speech, and Signal Processing 3. pp. 1845. Kang, S.H., et al., 2018. Optik 156, 197. Kim, D., et al., 2018. Optik 161, 270. Lim, K., et al., 2015. J. Comput. Assist. Tomogr. 39, 443. Moss, A.A., et al., 1981. Gastroenterology 80, 45. Muelleman, T.J., et al., 2016. J. Neurol. Surg. Part B Skull Base 77, 243. Rudin, L.I., et al., 1992. Physica D 60, 259. Seo, K., et al., 2016. J. Magn. 21, 593. Solomon, J., et al., 2014. Medical imaging 2014. Phys. Med. Imag. https://doi.org/10. 1117/12.2043555. Sundaram, K., et al., 2014. Int. J. Innov. Res. Sci. Eng. Technol. 3, 10333. Vishnukumar, S., et al., 2017. Opt. Commun. 404, 80. Wieneke, B., 2017. Exp. Fluid 58, 94.
Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This research was supported by the National Research Foundation of Korea (NRF-2016R1D1A1B03930357) and (NRF2019R1F1A1062811). Dong-Kyoon Han and Youngjin Lee contributed equally to the writing of this paper.
9