Article information

2025 , Volume 30, ¹ 2, p.126-139

Pham C.T., Tran T.T., Dinh H.H., Duong V.C., Phan M.C.

Computed tomography image reconstruction using graph total variation

In this paper, we propose a model that combines deep learning with graph total variation (GTV) for denoising computed tomography images. The GTV model employs two neural networks: one to represent pixel characteristics and construct a graph, and the other to generate the parameters for the model. Integration of the graph with the learned parameters yields highly effective results, as demonstrated in our experimental evaluations. Our findings indicate that the proposed method outperforms other related approaches in terms of performance.

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Keywords: convolutional neural network, total variation, graph total variation, computed tomography, image denoising, deep learning

doi: 10.25743/ICT.2025.30.2.010

Author(s):
Pham Cong Thang
Dr.
Position: Lecture
Office: Faculty of Information Technology, The University of Danang University of Science and Technology
Address: 550000, Vietnam, Danang, Nguyen Luong Bang st., 54
E-mail: pcthang@dut.udn.vn

Tran Thi Thu Thao
Position: Research Scientist
Office: Faculty of Statistics and Informatics, The University of Danang University of Economics
Address: 550000, Vietnam, Danang, Ngu Hanh Son st., 71
E-mail: thaotran@due.udn.vn

Dinh Huy Hoang
Position: Research Scientist
Office: Faculty of Information Technology, The University of Danang University of Science and Technology
Address: 550000, Vietnam, Danang, Nguyen Luong Bang st., 54

Duong Van Chon
Position: Research Scientist
Office: Faculty of Information Technology, The University of Danang University of Science and Technology
Address: 550000, Vietnam, Danang, Nguyen Luong Bang st., 54

Phan Manh Cuong
Position: Research Scientist
Office: Faculty of Information Technology, The University of Danang University of Science and Technology
Address: 550000, Vietnam, Danang, Nguyen Luong Bang st., 54

References:
[1] Pham C.T., Kopylov A.V. Multi-quadratic dynamic programming procedure of
edge preserving denoising for medical images. International Archives of the Photogram
metry, Remote Sensing and Spatial Information Sciences. 2015; (XL-5/W6):101–106.
DOI:10.5194/isprsarchives-XL-5-W6-101-2015.

[2] Pham C.T., Kopylov A.V., Dvoenko S.D. Edge-preserving denoising based on dy
namic programming on the full set of adjacency graphs. International Archives of the Pho
togrammetry, Remote Sensing and Spatial Information Sciences. 2017; (XLII-2/W4):55–60.
DOI:10.5194/isprs-archives-XLII-2-W4-55-2017.

[3] Liu Y. A Method of CT image denoising based on residual encoder-decoder network. Journal
of Healthcare Engineering. 2021: 1–9. DOI:10.1155/2021/2384493.

[4] Mohammadinejad P., Mileto A., Yu L., Leng Sh., Missert A.D., Jensen C.T.,
Gong H., McCollough C., Fletcher C. CT noise-reduction methods for lower-dose scan
ning: strengths and weaknesses of iterative reconstruction algorithms and new techniques.
Radiographics. 2021; 41(5):1493–1508. DOI:10.1148/rg.2021200196. Available at: https:
//pubs.rsna.org/doi/10.1148/rg.2021200196.

[5] Kang E., Min J., Ye J.C. A deep convolutional neural network using directional
wavelets for low-dose X-ray CT reconstruction. Medical Physics. 2017; 44(10):e360–e375.
DOI:10.1002/mp.12344. Available at: https://aapm.onlinelibrary.wiley.com/doi/full/
10.1002/mp.12344.

[6] Park S.B. Advances in deep learning for computed tomography denoising. World Journal of
Clinical Cases. 2021; 9(26):7614–7619. DOI:10.12998/wjcc.v9.i26.7614. Available at: https:
//www.wjgnet.com/2307-8960/coretip/v9/i26/7614.htm.

[7] Sadia R.T., Chen J., Zhang J. CT image denoising methods for image quality im
provement and radiation dose reduction. Journal of Applied Clinical Medical Physics. 2024;
25(2):1–17. DOI:10.1002/acm2.14270. Available at: https://aapm.onlinelibrary.wiley.
com/doi/full/10.1002/acm2.14270.

[8] Zhang H., Zeng D., Zhang H., Wang J., Liang Z., Ma J. Applications of non
local means algorithm in low-dose X-ray CT image processing and reconstruction: a re
view. Medical Physics. 2017; 44(3):1168–1185. DOI:10.1002/mp.12097. Available at: https:
//aapm.onlinelibrary.wiley.com/doi/full/10.1002/mp.12097.

[9] Lepcha D.C., Dogra A., Goyal B., Goyal V., Kukreja V., Bavirisetti D.P. Aconstruc
tive non-local means algorithm for low-dose computed tomog raphy denoising with morpholog
ical residual processing. PLoS One. 2023; 18(9):e0291911. DOI:10.1371/journal.pone.0291911.
Available at: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.
0291911.

[10] Wang G., Guo S., Han L., Cekderi A.B., Song X., Zhao Z. Asymp
tomatic COVID-19 CT image denoising method based on wavelet transform combined
with improved PSO. Biomedical Signal Processing and Control. 2022; (76):103707.
DOI:10.1016/j.bspc.2022.103707. Available at: https://www.sciencedirect.com/science/
article/pii/S1746809422002294.

[11] Abuya T.K., Rimiru R.M., Okeyo G.O. An image denoising technique using wavelet
anisotropic Gaussian filter-based denoising convolutional neural network for CT images. Ap
plied Sciences. 2023; 13(21):1–23. DOI:10.3390/app132112069.

[12] Luo P., Qu X., Qing X., Gu J. CT image denoising using double density dual tree complex
wavelet with modified thresholding. 2018 2nd International Conference on Data Science and
Business Analytics (ICDSBA). 2018: 287–290. DOI:10.1109/ICDSBA.2018.0038. Available at:
https://ieeexplore.ieee.org/document/8588929.

[13] Ertas M., Akan A., Yildirim I., Kamasak M. Image denoising by using non-local means
and total variation. 22nd Signal Processing and Communications Applications Conference.
2014: 2122–2125. DOI:10.1109/SIU.2014.6830681. Available at: https://ieeexplore.ieee.
org/document/6830681.

[14] Sagheer S.V.M., George S.N. Denoising of low-dose CT images via low-rank ten
sor modeling and total variation regularization. Artificial Intelligence in Medicine. 2019;
(94):1–17. DOI:10.1016/j.artmed.2018.12.006. Available at: https://www.sciencedirect.
com/science/article/pii/S093336571730636X.

[15] Tran T.T.T., Pham C.T., Kopylov A.V., Nguyen V.N. An adaptive variational model
for medical images restoration. International Archives of the Photogrammetry, Remote Sensing
and Spatial Information Sciences. 2019; (XLII-2/W12):219–224. DOI:10.5194/isprs-archives
XLII-2-W12-219-2019.

[16] Yan R., Liu Y., Liu Y., Wang L., Zhao R., Bai Y., Gui Z. Image denoising for
low-dose CT via convolutional dictionary learning and neural network. IEEE Transactions
on Computational Imaging. 2023; (9):83–93. DOI:10.1109/TCI.2023.3241546. Available at:
https://ieeexplore.ieee.org/document/10036072.

[17] Zhang Y., Mou X., Wang G., Yu H. Tensor-based dictionary learning for spectral
CT reconstruction. IEEE Transactions on Medical Imaging. 2017; 36(1):142–154. DOI:10.
1109/TMI.2016.2600249. Available at: https://ieeexplore.ieee.org/document/7542501.

[18] Xu Y., Li Z., Zhang X., Fan W., Zhou C., Que D., Yuan J., He Q., Liang D.,
Liu X., Zheng H., Hu Z., Zhang N. Low-dose PET image denoising based on cou
pled dictionary learning. Nuclear Instruments and Methods in Physics Research. Section A:
Accelerators, Spectrometers, Detectors and Associated Equipment. 2021; (1020):165908.
DOI:10.1016/j.nima.2021.165908. Available at: https://www.sciencedirect.com/science/
article/pii/S0168900221008780.

[19] Jiang C., Zhang Q., Fan R., Hu Z. Super-resolution CT image reconstruc
tion based on dictionary learning and sparse representation. Scientific Reports. 2018;
(8):1–10. DOI:10.1038/s41598-018-27261-z. Available at:
https://www.nature.com/
articles/s41598-018-27261-z.pdf.

[20] Bai J., Song S., Fan T., Jiao L. Medicalimagedenoising based on sparse dictionary learning
and cluster ensemble. Soft Computing. 2017; (22):1467–1473. DOI:10.1007/s00500-017-2853-7.
Available at: https://link.springer.com/article/10.1007/s00500-017-2853-7.

[21] Song Y., Ge C., Song N., Deng M. A novel dictionary learning-based approach
for ultrasound elastography denoising. Mathematical Biosciences and Engineering. 2022;
19(11):11533–11543. DOI:10.3934/mbe.2022537. Available at: https://www.aimspress.com/
article/doi/10.3934/mbe.2022537.

[22] Chen L.L., Gou S.P., Yao Y., Bai J., Jiao L., Sheng K. Denoising of low dose
CT image with context-based BM3D. 2016 IEEE Region 10 Conference (TENCON). 2016:
682–685. DOI:10.1109/TENCON.2016.7848089. Available at: https://ieeexplore.ieee.
org/document/7848089.

[23] Zhao T., Hoffman J., Mcnitt-Gray M., Ruan D. Ultra-low-dose CT image denoising
using modified BM3D scheme tailored to datastatistics. Medical Physics. 2019; 46(1):190–198.
DOI:10.1002/mp.13252. Available at: https://aapm.onlinelibrary.wiley.com/doi/abs/
10.1002/mp.13252.

[24] Do Y., Cho Y., Kang S.H., Lee Y. Optimization of block-matching and
3D filtering (BM3D) algorithm in brain SPECT imaging using fan beam collima
tor:
phantom study. Nuclear Engineering and Technology. 2022; 54(9):3403–3414.
DOI:10.1016/j.net.2022.04.008. Available at: https://www.sciencedirect.com/science/
article/pii/S173857332200211X.

[25] Hashemi S.M, Paul N.S., Beheshti S., Cobbold R.S.C. Adaptively tuned itera
tive low dose CT image denoising. Computational and Mathematical Methods in Medicine.
2015: 638568. DOI:0.1155/2015/638568. Available at: https://pubmed.ncbi.nlm.nih.gov/
26089972.

[26] Pang J., Cheung G. Graph laplacian regularization for image denoising: analysis in the
continuous domain. IEEE Transactions on Image Processing. 2017; 26(4):1770–1785. DOI:10.
1109/TIP.2017.2651400. Available at: https://ieeexplore.ieee.org/document/7814302.

[27] Ortega A., Frossard P., Kovacevic J., Moura J.M.F., Vandergheynst P. Graph
signal processing: overview, challenges, and applications. Proceedings of the IEEE. 2018;
106(5):808–828. DOI:10.1109/JPROC.2018.2820126. Available at: https://ieeexplore.
ieee.org/document/8347162.

[28] Zeng J., Cheung G., Ng M., Pang J., Yang C. 3D point cloud denoising using
graph laplacian regularization of a low dimensional manifold model. IEEE Transactions
on Image Processing. 2020; (29):3474–3489. DOI:10.1109/TIP.2019.2961429. Available at:
https://ieeexplore.ieee.org/document/8945167.

[29] Bai Y., Cheung G., Liu X., Gao W. Graph-based blind image deblurring from
a single photograph. IEEE Transactions on Image Processing. 2019; 28(3):1404–1418.
DOI:10.1109/TIP.2018.2874290. Available at: https://ieeexplore.ieee.org/abstract/
document/8488519.

[30] Zeng J., Pang J., Sun W., Cheung G. Deep graph laplacian regularization for robust
denoising of real images. 2019 IEEE/CVF Conference on Computer Vision and Pattern Recog
nition Workshops (CVPRW). 2019: 1759–1768. DOI:10.1109/CVPRW.2019.00226. Available
at: https://ieeexplore.ieee.org/document/9025512.

[31] Zhang K., Zuo W., Chen Y., Meng D., Zhang L. Beyond a gaussian denoiser: residual
learning of deep CNN for image denoising. IEEE Transactions on Image Processing. 2017;
26(7):3142–3155. DOI:10.1109/TIP.2017.2662206. Available at: https://ieeexplore.ieee.
org/abstract/document/7839189.

[32] Vu H., Cheung G., Eldar Y.C. Unrolling of deep graph total variation for image de
noising. 2021 IEEE International Conference on Acoustics, Speech and Signal Processing
(ICASSP). 2021: 2050–2054. DOI:10.1109/ICASSP39728.2021.9414453. Available at: https:
//ieeexplore.ieee.org/document/9414453.

[33] Dabov K., Foi A., Katkovnik V., Egiazarian K. Image denoising by sparse 3-D
transform-domain collaborative filtering. IEEE Transactions on Image Processing. 2007;
16(8):2080–2095. DOI:10.1109/TIP.2007.901238. Available at: https://ieeexplore.ieee.
org/document/4271520.

[34] Elad M., Aharon M. Image denoising via sparse and redundant representations over
learned dictionaries. IEEE Transactions on Image Processing. 2006; 15(12):3736–3745. DOI:10.
1109/TIP.2006.881969. Available at: https://ieeexplore.ieee.org/document/4011956.

[35] Pham C.T., Kopylov A.V. Parametric procedures for image denoising with flexible prior
model. SoICT’16: Proceedings of the 7th Symposium on Information and Communication
Technology. 2016: 294–301. DOI:10.1145/3011077.3011099. Available at: https://dl.acm.
org/doi/10.1145/3011077.3011099.

[36] Berger P., Hannak G., Matz G. Graph signal recovery via primal-dual algorithms for
total variation minimization. IEEE Journal of Selected Topics in Signal Processing. 2017;
11(6):842–855. DOI:10.1109/JSTSP.2017.2726978. Available at: https://ieeexplore.ieee.
org/abstract/document/7979518.

[37] Gonzalez R.C., Woods R.E. Digital image processing. 2nd Ed. Prentice Hall; 2002: 816.

[38] Bovik A.C. Handbook of image and video processing (2nd ed.). Academic Press; 2005: 1384.

[39] Wang Z., Bovik A.C. Modern image quality assessment. Morgan & Claypool Publish
ers; 2006: 146. DOI:10.2200/S00010ED1V01Y200508IVM003. Available at: https://link.
springer.com/book/10.1007/978-3-031-02238-8.

[40] Li L., Yu X., Jin Z., Zhao Z., Zhuang X., Liu Z. FDnCNN-based image
denoising for multi-labfel localization measurement. Measurement. 2020; (152):107367.
DOI:10.1016/j.measurement.2019.107367. Available at: https://www.sciencedirect.com/
science/article/pii/S026322411931231X.

[41] Zhang K., Zuo W., Zhang L. FFDNet: toward a fast and flexible solution for CNN
based image denoising. IEEE Transactions on Image Processing. 2018; 27(9):4608–4622.
DOI:10.1109/TIP.2018.2839891. Available at: https://ieeexplore.ieee.org/abstract/
document/8365806.

[42] Zhang K., Zuo W., Gu S., Zhang L. Learning deep CNN denoiser prior for image
restoration. 2017 IEEE Conference on Computer Vision and Pattern Recognition. 2017:
2808–2817. DOI:10.1109/CVPR.2017.300. Available at: https://www.computer.org/csdl/
proceedings-article/cvpr/2017/0457c808/12OmNqyDjmT

Bibliography link:
Pham C.T., Tran T.T., Dinh H.H., Duong V.C., Phan M.C. Computed tomography image reconstruction using graph total variation // Computational technologies. 2025. V. 30. ¹ 2. P. 126-139
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