[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ skip to main content
research-article

Denoising of low-dose CT images via low-rank tensor modeling and total variation regularization

Published: 01 March 2019 Publication History

Highlights

A new denoising method for Computed tomography (CT) images based on low-rank approximation by modeling the global spatial correlation and local smoothness properties is proposed.
The tensor nuclear norm is used to describe the global properties and the tensor total variation is used to characterize the local smoothness.
An efficient algorithm for solving the resulting optimization problem based on the Alternative Direction Method of Multipliers (ADMM) is also developed.
The experiments explain the applicability of proposed method for real medical CT images.
The proposed algorithm is shown to have superior performance compared to the state-of-art works existing in the literature.

Abstract

Low-dose Computed Tomography (CT) imaging is a most commonly used medical imaging modality. Though the reduction in dosage reduces the risk due to radiation, it leads to an increase in noise level. Hence, it is a mandatory requirement to include a noise reduction technique as a pre- and/or post-processing step for better disease diagnosis. The nuclear norm minimization has attracted a great deal of research interest in contemporary years. This paper proposes a low-rank approximation based approach for denoising of CT images by effectively utilizing the global spatial correlation and local smoothness properties. The tensor nuclear norm is used to describe the global properties and the tensor total variation is used to characterize the local smoothness as well as to improve global smoothness. The resulting optimization problem is solved by the Alternative Direction Method of Multipliers (ADMM) technique. Experimental results on simulated and real CT data prove that the proposed methods outperform the state-of-art works.

References

[1]
A. Borsdorf, R. Raupach, T. Flohr, J. Hornegger, Wavelet based noise reduction in ct-images using correlation analysis, IEEE Trans Med Imaging 27 (12) (2008) 1685–1703.
[2]
R.J. Geraldo, L.M. Cura, P.E. Cruvinel, N.D. Mascarenhas, Low dose ct filtering in the image domain using map algorithms, IEEE Trans Radiat Plasma Med Sci 1 (1) (2017) 56–67.
[3]
M.F. Rahiman, R.A. Rahim, Z. Zakaria, Design and modelling of ultrasonic tomography for two-component high-acoustic impedance mixture, Sens Actuators A: Phys 147 (2) (2008) 409–414.
[4]
Y. Chen, L. Shi, Q. Feng, J. Yang, H. Shu, L. Luo, J.-L. Coatrieux, W. Chen, Artifact suppressed dictionary learning for low-dose ct image processing, IEEE Trans Med Imaging 33 (12) (2014) 2271–2292.
[5]
Q. Ding, Y. Long, X. Zhang, J.A. Fessler, Statistical Image Reconstruction Using Mixed Poisson-Gaussian Noise Model for X-ray CT, 2018, arXiv preprint arXiv:1801.09533.
[6]
D.-H. Trinh, T.-T. Nguyen, N. Linh-Trung, An effective example-based denoising method for ct images using Markov random field, Advanced Technologies for Communications (ATC), 2014 International Conference on, IEEE (2014) 355–359.
[7]
P. Gravel, G. Beaudoin, J.A. De Guise, A method for modeling noise in medical images, IEEE Trans Med Imaging 23 (10) (2004) 1221–1232.
[8]
T.-T. Nguyen, D.-H. Trinh, N. Linh-Trung, An efficient example-based method for ct image denoising based on frequency decomposition and sparse representation, Advanced Technologies for Communications (ATC), 2016 International Conference on, IEEE (2016) 293–296.
[9]
M. Diwakar, M. Kumar, Edge preservation based ct image denoising using wiener filtering and thresholding in wavelet domain, Parallel, Distributed and Grid Computing (PDGC), 2016 Fourth International Conference on, IEEE (2016) 332–336.
[10]
S. Hashemi, N.S. Paul, S. Beheshti, R.S. Cobbold, Adaptively tuned iterative low dose ct image denoising, Comput Math Methods Med (2015).
[11]
H. Chen, Y. Zhang, W. Zhang, P. Liao, K. Li, J. Zhou, G. Wang, Low-dose ct denoising with convolutional neural network, Biomedical Imaging (ISBI 2017), 2017 IEEE 14th International Symposium on, IEEE (2017) 143–146.
[12]
Y. Wang, S. Fu, W. Li, C. Zhang, An adaptive nonlocal filtering for low-dose ct in both image and projection domains, J Comput Des Eng 2 (2) (2015) 113–118.
[13]
H. Rabbani, R. Nezafat, S. Gazor, Wavelet-domain medical image denoising using bivariate Laplacian mixture model, IEEE Trans Biomed Eng 56 (12) (2009) 2826–2837.
[14]
V. Davidoiu, L. Hadjilucas, I. Teh, N.P. Smith, J.E. Schneider, J. Lee, Evaluation of noise removal algorithms for imaging and reconstruction of vascular networks using micro-CT, Biomed Phys Eng Express 2 (4) (2016) 045015.
[15]
L. Chen, S. Gou, Y. Yao, J. Bai, L. Jiao, K. Sheng, Denoising of low dose ct image with context-based bm3d, Region 10 Conference (TENCON), 2016 IEEE, IEEE (2016) 682–685.
[16]
T. Lei, W. Sewchand, Statistical approach to X-ray CT imaging and its applications in image analysis. I. Statistical analysis of X-ray CT imaging, IEEE Trans Med Imaging 11 (1) (1992) 53–61.
[17]
W. Yang, H. Zhang, J. Yang, J. Wu, X. Yin, Y. Chen, H. Shu, L. Luo, G. Coatrieux, Z. Gui, et al., Improving low-dose CT image using residual convolutional network, IEEE Access 5 (2017) 24698–24705.
[18]
B. Mao, D. Xiao, X. Xiong, X. Chen, W. Zhang, Y. Kang, Denoising low dose ct images via 3d total variation using CUDA, Medical Imaging Physics and Engineering (ICMIPE), 2013 IEEE International Conference on, IEEE (2013) 47–50.
[19]
J. Liu, J. Ma, Y. Zhang, Y. Chen, J. Yang, H. Shu, L. Luo, G. Coatrieux, W. Yang, Q. Feng, et al., Discriminative feature representation to improve projection data inconsistency for low dose ct imaging, IEEE Trans Med Imaging 36 (12) (2017) 2499–2509.
[20]
D.L. Donoho, Compressed sensing, IEEE Trans Inf Theory 52 (4) (2006) 1289–1306.
[21]
H. Yu, G. Wang, Compressed sensing based interior tomography, Phys Med Biol 54 (9) (2009) 2791.
[22]
J. Liu, Y. Hu, J. Yang, Y. Chen, H. Shu, L. Luo, Q. Feng, Z. Gui, G. Coatrieux, 3d feature constrained reconstruction for low dose ct imaging, IEEE Trans Circ Syst Video Technol 28 (5) (2018) 1232–1247.
[23]
Y. Chen, D. Gao, C. Nie, L. Luo, W. Chen, X. Yin, Y. Lin, Bayesian statistical reconstruction for low-dose X-ray computed tomography using an adaptive-weighting nonlocal prior, Comput Med Imaging Graph 33 (7) (2009) 495–500.
[24]
Y. Chen, W. Chen, X. Yin, X. Ye, X. Bao, L. Luo, Q. Feng, X. Yu, et al., Improving low-dose abdominal ct images by weighted intensity averaging over large-scale neighborhoods, Eur J Radiol 80 (2) (2011) e42–e49.
[25]
Y. Chen, J. Ma, Q. Feng, L. Luo, P. Shi, W. Chen, Nonlocal prior Bayesian tomographic reconstruction, J Math Imaging Vis 30 (2) (2008) 133–146.
[26]
H. Watanabe, M. Kanematsu, T. Miyoshi, S. Goshima, H. Kondo, N. Moriyama, K.T. Bae, Improvement of image quality of low radiation dose abdominal ct by increasing contrast enhancement, Am J Roentgenol 195 (4) (2010) 986–992.
[27]
Y. Chen, J. Liu, Y. Hu, J. Yang, L. Shi, H. Shu, Z. Gui, G. Coatrieux, L. Luo, Discriminative feature representation: an effective postprocessing solution to low dose ct imaging, Phys Med Biol 62 (6) (2017) 2103.
[28]
J. Cao, Q. Zhao, L. Gui, Tensor denoising using Bayesian cp factorization, Information Science and Technology (ICIST), 2016 Sixth International Conference on, IEEE (2016) 49–54.
[29]
D. Strong, T. Chan, Edge-preserving and scale-dependent properties of total variation regularization, Inverse Probl 19 (6) (2003) S165.
[30]
N. Kishore Kumar, J. Schneider, Literature survey on low rank approximation of matrices, Linear Multilinear Algebra (2016) 1–33.
[31]
Q. Ke, T. Kanade, Robust l 1 norm factorization in the presence of outliers and missing data by alternative convex programming, in: 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), vol. 1, IEEE, 2005, pp. 739–746.
[32]
A.M. Buchanan, A.W. Fitzgibbon, Damped Newton algorithms for matrix factorization with missing data, in: 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), vol. 2, IEEE, 2005, pp. 316–322.
[33]
N. Srebro, T. Jaakkola, et al., Weighted low-rank approximations, ICML, vol. 3 (2003) 720–727.
[34]
J. Wright, A. Ganesh, S. Rao, Y. Peng, Y. Ma, Robust principal component analysis: exact recovery of corrupted low-rank matrices via convex optimization, Advances in Neural Information Processing Systems (2009) 2080–2088.
[35]
E.J. Candès, X. Li, Y. Ma, J. Wright, Robust principal component analysis?, J ACM (JACM) 58 (3) (2011) 11.
[36]
M. Fazel, H. Hindi, S.P. Boyd, A rank minimization heuristic with application to minimum order system approximation, in: American Control Conference, 2001. Proceedings of the 2001, vol. 6, IEEE, 2001, pp. 4734–4739.
[37]
E.J. Candes, Y. Plan, Matrix completion with noise, Proc IEEE 98 (6) (2010) 925–936.
[38]
S.V.M. Sagheer, S.N. George, Ultrasound image despeckling using low rank matrix approximation approach, Biomed Signal Process Control 38 (2017) 236–249.
[39]
J.-F. Cai, E.J. Candès, Z. Shen, A singular value thresholding algorithm for matrix completion, SIAM J Optim 20 (4) (2010) 1956–1982.
[40]
Z. Zhang, S. Aeron, Denoising and completion of 3d data via multidimensional dictionary learning, 2015, arXiv preprint arXiv:1512.09227.
[41]
J.D. Carroll, J.-J. Chang, Analysis of individual differences in multidimensional scaling via an n-way generalization of “eckart-young” decomposition, Psychometrika 35 (3) (1970) 283–319.
[42]
L.R. Tucker, Some mathematical notes on three-mode factor analysis, Psychometrika 31 (3) (1966) 279–311.
[43]
L. De Lathauwer, B. De Moor, J. Vandewalle, A multilinear singular value decomposition, SIAM J Matrix Anal Appl 21 (4) (2000) 1253–1278.
[44]
M.E. Kilmer, C.D. Martin, L. Perrone, A Third-order Generalization of the Matrix SVD as a Product of Third-order Tensors, Tufts University, Department of Computer Science, 2018, Tech. Rep. TR-2008-4.
[45]
W. He, H. Zhang, L. Zhang, H. Shen, Total-variation-regularized low-rank matrix factorization for hyperspectral image restoration, IEEE Trans Geosci Rem Sens 54 (1) (2016) 178–188.
[46]
B. Li, D. Que, Medical images denoising based on total variation algorithm, Procedia Environ Sci 8 (2011) 227–234.
[47]
S. Yang, J. Wang, W. Fan, X. Zhang, P. Wonka, J. Ye, An efficient ADMM algorithm for multidimensional anisotropic total variation regularization problems, Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, ACM (2013) 641–649.
[48]
M. Baburaj, S.N. George, Twist tensor total variation regularized-reweighted nuclear norm based tensor completion for video missing area recovery, Inf Sci (2018).
[49]
Z. Lin, M. Chen, Y. Ma, The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices, 2010, arXiv preprint arXiv:1009.5055.
[50]
M. Makitalo, A. Foi, Optimal inversion of the generalized Anscombe transformation for Poisson-Gaussian noise, IEEE Trans Image Process 22 (1) (2013) 91–103.
[51]
J. Zhang, Y. Chen, L. Luo, Improved nonlocal means for low-dose X-ray ct image, Information Science and Control Engineering (ICISCE), 2016 3rd International Conference on, IEEE (2016) 410–413.
[52]
Y. Wang, S. Fu, W. Li, C. Zhang, An adaptive nonlocal filtering for low-dose ct in both image and projection domains, J Comput Des Eng 2 (2) (2015) 113–118.
[53]
M. Elad, M. Aharon, Image denoising via sparse and redundant representations over learned dictionaries, IEEE Trans Image Process 15 (12) (2006) 3736–3745.
[54]
K. Dabov, A. Foi, V. Katkovnik, K. Egiazarian, Image denoising by sparse 3-d transform-domain collaborative filtering, IEEE Trans Image Process 16 (8) (2007) 2080–2095.
[55]
J. Zhang, G. Lin, L. Wu, C. Wang, Y. Cheng, Wavelet and fast bilateral filter based de-speckling method for medical ultrasound images, Biomed Signal Process Control 18 (2015) 1–10.
[56]
F. Sattar, L. Floreby, G. Salomonsson, B. Lovstrom, Image enhancement based on a nonlinear multiscale method, IEEE Trans Image Process 6 (6) (1997) 888–895.
[57]
L. Zhang, L. Zhang, X. Mou, D. Zhang, FSIM: a feature similarity index for image quality assessment, IEEE Trans Image Process 20 (8) (2011) 2378–2386.
[58]
Q. Wei, J. Bioucas-Dias, N. Dobigeon, J.-Y. Tourneret, Hyperspectral and multispectral image fusion based on a sparse representation, IEEE Trans Geosci Rem Sens 53 (7) (2015) 3658–3668.
[59]
G. Blanchet, L. Moisan, An explicit sharpness index related to global phase coherence, Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE International Conference on, IEEE (2012) 1065–1068.
[60]
Y. Chen, Z. Yang, Y. Hu, G. Yang, Y. Zhu, Y. Li, W. Chen, C. Toumoulin, et al., Thoracic low-dose ct image processing using an artifact suppressed large-scale nonlocal means, Phys Med Biol 57 (9) (2012) 2667.
[61]
W. Hu, D. Tao, W. Zhang, Y. Xie, Y. Yang, The twist tensor nuclear norm for video completion, IEEE Trans Neural Netw Learn Syst 28 (12) (2017) 2961–2973.

Cited By

View all
  • (2024)Irregular feature enhancer for low-dose CT denoisingMultimedia Systems10.1007/s00530-024-01575-730:6Online publication date: 25-Nov-2024
  • (2023)Low-Rank Tensor Data Reconstruction and Denoising via ADMM: Algorithm and Convergence AnalysisJournal of Scientific Computing10.1007/s10915-023-02364-697:2Online publication date: 7-Oct-2023
  • (2022)A review on self-adaptation approaches and techniques in medical image denoising algorithmsMultimedia Tools and Applications10.1007/s11042-022-13511-w81:26(37591-37626)Online publication date: 1-Nov-2022

Index Terms

  1. Denoising of low-dose CT images via low-rank tensor modeling and total variation regularization
          Index terms have been assigned to the content through auto-classification.

          Recommendations

          Comments

          Please enable JavaScript to view thecomments powered by Disqus.

          Information & Contributors

          Information

          Published In

          cover image Artificial Intelligence in Medicine
          Artificial Intelligence in Medicine  Volume 94, Issue C
          Mar 2019
          153 pages

          Publisher

          Elsevier Science Publishers Ltd.

          United Kingdom

          Publication History

          Published: 01 March 2019

          Author Tags

          1. Computed tomography image
          2. Denoising
          3. Tensor low rank recovery
          4. Tensor total variation

          Qualifiers

          • Research-article

          Contributors

          Other Metrics

          Bibliometrics & Citations

          Bibliometrics

          Article Metrics

          • Downloads (Last 12 months)0
          • Downloads (Last 6 weeks)0
          Reflects downloads up to 28 Jan 2025

          Other Metrics

          Citations

          Cited By

          View all
          • (2024)Irregular feature enhancer for low-dose CT denoisingMultimedia Systems10.1007/s00530-024-01575-730:6Online publication date: 25-Nov-2024
          • (2023)Low-Rank Tensor Data Reconstruction and Denoising via ADMM: Algorithm and Convergence AnalysisJournal of Scientific Computing10.1007/s10915-023-02364-697:2Online publication date: 7-Oct-2023
          • (2022)A review on self-adaptation approaches and techniques in medical image denoising algorithmsMultimedia Tools and Applications10.1007/s11042-022-13511-w81:26(37591-37626)Online publication date: 1-Nov-2022

          View Options

          View options

          Figures

          Tables

          Media

          Share

          Share

          Share this Publication link

          Share on social media