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Sinogram restoration for low-dose X-ray computed tomography using regularized Perona–Malik equation with intuitionistic fuzzy entropy

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Abstract

Edges and flat areas in the sinogram of low-dose X-ray computed tomography are difficult to distinguish. This lack of distinction leads to excessive smoothing in the sinogram restoration. To address this problem, we propose a sinogram restoration algorithm using the regularized Perona–Malik (P–M) equation with intuitionistic fuzzy entropy. Firstly, considering the sinogram fuzziness, a novel edge indicator function is constructed using both the gradient magnitude and intuitionistic fuzzy entropy. Secondly, using the constructed edge indicator function as the diffusion coefficient, a novel regularized P–M equation smoothing model is presented. The proposed model overcomes the shortage of traditional P–M equations, which are ill-conditioned. Moreover, it performs diffusion with different directions and intensities in different regions of the sinogram. The optimal solution of the proposed algorithm is obtained by using the additional operator splitting method. Finally, the reconstructed image is achieved by filtered back projection from the smoothed sinogram. Experimental results show that the presented method can retain important edges while smoothing noise and perform better than others.

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References

  1. Seeram, E.: Computed tomography: physical principles, clinical applications, and quality control. Elsevier, Amsterdam (2015)

    Google Scholar 

  2. Pearce, M.S., Salotti, J.A., Little, M.P., et al.: Radiation exposure from CT scans in childhood and subsequent risk of leukaemia and brain tumours: a retrospective cohort study. The Lancet 380(9840), 499–505 (2012)

    Article  Google Scholar 

  3. Shangguan, H., Zhang, Q., Liu, Y., et al.: Low-dose CT statistical iterative reconstruction via modified MRF regularization. Comput. Methods Programs Biomed. 123, 129–141 (2016)

    Article  Google Scholar 

  4. Nguyen, T.A., Nakib, A., Nguyen, H.N.: Medical image denoising via optimal implementation of non-local means on hybrid parallel architecture. Comput. Methods Programs Biomed. 129, 29–39 (2016)

    Article  Google Scholar 

  5. Zhang, H., Ouyang, L., Ma, J., et al.: Noise correlation in CBCT projection data and its application for noise reduction in low-dose CBCT. Med. Phys. 41(3), 031906 (2014)

    Article  Google Scholar 

  6. Balda, M., Hornegger, J., Heismann, B.: Ray contribution masks for structure adaptive sinogram filtering. IEEE Trans. Med. Imaging 31(6), 1228–1239 (2012)

    Article  Google Scholar 

  7. Zhang, Q., Gui, Z., Chen, Y., et al.: Bayesian sinogram smoothing with an anisotropic diffusion weighted prior for low-dose X-ray computed tomography. Opt. Int. J. Light Electron Opt. 124(17), 2811–2816 (2013)

    Article  Google Scholar 

  8. Beister, M., Kolditz, D., Kalender, W.A.: Iterative reconstruction methods in X-ray CT. Phys. Med. 28(2), 94–108 (2012)

    Article  Google Scholar 

  9. Chen, Y., Shi, L., Feng, Q., et al.: Artifact suppressed dictionary learning for low-dose CT image processing. IEEE Trans. Med. Imaging 33(12), 2271–2292 (2014)

    Article  Google Scholar 

  10. Zeng, G.L.: Noise-weighted spatial domain FBP algorithm. Med. Phys. 41(5), 051906 (2014)

    Article  Google Scholar 

  11. Wang, J.: Noise reduction for low-dose X-ray computed tomography. Ph.D. Thesis. State University of New York, Stony Brook (2006)

  12. Wang, J., Li, T., Liang, Z., et al.: Dose reduction for kilovotage cone-beam computed tomography in radiation therapy. Phys. Med. Biol. 53(11), 2897 (2008)

    Article  Google Scholar 

  13. Wang, J., Lu, H., Wen, J., et al.: Multiscale penalized weighted least-squares sinogram restoration for low-dose X-ray computed tomography. IEEE Trans. Biomed. Eng. 55(3), 1022–1031 (2008)

    Article  Google Scholar 

  14. Zhang, Y., Zhang, J., Lu, H.: Statistical sinogram smoothing for low-dose CT with segmentation-based adaptive filtering. IEEE Trans. Nucl. Sci. 57(5), 2587–2598 (2010)

    Article  Google Scholar 

  15. Cui, X., Gui, Z., Zhang, Q., et al.: The statistical sinogram smoothing via adaptive-weighted total variation regularization for low-dose X-ray CT. Opt. Int. J. Light Electron Opt. 125(18), 5352–5356 (2014)

    Article  Google Scholar 

  16. Hsieh, J.: Adaptive streak artifact reduction in computed tomography resulting from excessive x-ray photon noise. Med. Phys. 25(11), 2139–2147 (1998)

    Article  Google Scholar 

  17. Kachelrieβ, M., Watzke, O., Kalender, W.A.: Generalized multi-dimensional adaptive filtering for conventional and spiral single-slice, multi-slice, and cone-beam CT. Med. Phys. 28(4), 475–490 (2001)

    Article  Google Scholar 

  18. Liu, Y., Zhang, Q., Gui, Z., et al.: Noise reduction for low-dose CT Sinogram based on fuzzy entropy. J. Electron. Inf. Technol. 35(6), 1421–1427 (2013)

    Article  Google Scholar 

  19. Liu, Y., Gui, Z., Zhang, Q.: Noise reduction for low-dose X-ray CT based on fuzzy logical in stationary wavelet domain. Opt. Int. J. Light Electron Opt. 124(18), 3348–3352 (2013)

    Article  Google Scholar 

  20. Szmidt, E., Kacprzyk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst. 118(3), 467–477 (2001)

    Article  MathSciNet  Google Scholar 

  21. Vlachos, I.K., Sergiadis, G.D.: Inner product based entropy in the intuitionistic fuzzy setting. Int. J. Uncertain Fuzziness Knowl. Based Syst. 14(03), 351–366 (2006)

    Article  MathSciNet  Google Scholar 

  22. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)

    Article  Google Scholar 

  23. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990)

    Article  Google Scholar 

  24. Catté, F., Lions, P.L., Morel, J.M., et al.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29(1), 182–193 (1992)

    Article  MathSciNet  Google Scholar 

  25. Weickert, J., Romeny, B.M.T.H., Viergever, M.A.: Efficient and reliable schemes for nonlinear diffusion filtering. IEEE Trans. Image Process. 7(3), 398–410 (1998)

    Article  Google Scholar 

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Acknowledgements

The work reported here was supported by the National Key Scientific Instrument and Equipment Development Project (2014YQ24044508); the National Key Research and Development Program of China (2016YFC0101602); the Natural Science Foundation of Shanxi Province (2015011046); the Shanxi Province Science Foundation for Youths (201601D021080, 201701D221106); and the Taiyuan University of Science and Technology doctoral promoter (20162044, 20152020). The authors thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of this paper.

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Authors and Affiliations

  1. School of Electronic Information Engineering, Taiyuan University of Science and Technology, Taiyuan, 030024, China

    Hong Shangguan, Xiong Zhang & Xueying Cui

  2. Shanxi Provincial Key Laboratory for Biomedical Imaging and Big Data, North University of China, Taiyuan, 030051, China

    Hong Shangguan, Yi Liu, Quan Zhang & Zhiguo Gui

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  1. Hong Shangguan
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  2. Xiong Zhang
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  3. Xueying Cui
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  4. Yi Liu
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  5. Quan Zhang
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  6. Zhiguo Gui
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Correspondence to Zhiguo Gui.

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Shangguan, H., Zhang, X., Cui, X. et al. Sinogram restoration for low-dose X-ray computed tomography using regularized Perona–Malik equation with intuitionistic fuzzy entropy. SIViP 13, 1511–1519 (2019). https://doi.org/10.1007/s11760-019-01496-3

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