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.
[link to elibrary.ru]
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
|