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A Regularized Limited-Angle CT Reconstruction Model Based on Sparse Multi-level Information Groups of the Images

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Image and Graphics Technologies and Applications (IGTA 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1480))

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Abstract

Restricted by the scanning environment and the shape of the target to be detected, the obtained projection data from computed tomography (CT) are usually incomplete, which leads to a seriously ill-posed problem, such as limited-angle CT reconstruction. In this situation, the classical filtered back-projection (FBP) algorithm loses efficacy especially when the scanning angle is seriously limited. By comparison, the simultaneous algebraic reconstruction technique (SART) can deal with the noise better than FBP, but it is also interfered by the limited-angle artifacts. At the same time, the total variation (TV) algorithm has the ability to address the limited-angle artifacts, since it takes into account a priori information about the target to be reconstructed, which alleviates the ill-posedness of the problem. Nonetheless, the current algorithms exist limitations when dealing with the limited-angle CT reconstruction problem. This paper analyses the distribution of the limited-angle artifacts, and it emerges globally. Then, motivated by TV algorithm, tight frame wavelet decomposition and group sparsity, this paper presents a regularization model based on sparse multi-level information groups of the images to address the limited-angle CT reconstruction, and the corresponding algorithm called modified proximal alternating linearized minimization (MPALM) is presented to deal with the proposed model. Numerical implementations demonstrate the effectiveness of the presented algorithms compared with the above classical algorithms.

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References

  1. Era, T.: Computed Tomography (2021)

    Google Scholar 

  2. Yumeng, G., Li, Z., et al.: Image reconstruction method for exterior circular cone-beam CT based on weighted directional total variation in cylindrical coordinates. J. Inverse Ill-posed Prob. 28(2), 155–172 (2020)

    Article  MathSciNet  Google Scholar 

  3. Noo, F., et al.: Image reconstruction from fan-beam projections on less than a short scan. Phys. Med. Biol. 47(14), 2525–2546 (2002)

    Article  Google Scholar 

  4. Brenner, D.J., Hall, E.J.: Computed tomography–an increasing source of radiation exposure. N. Engl. J. Med. 357(22), 2277–2284 (2013)

    Article  Google Scholar 

  5. Berrington, G.D.A., et al.: Projected cancer risks from computed tomographic scans performed in the United States in 2007. Arch. Intern. Med. 169(22), 2071–7 (2009)

    Google Scholar 

  6. Jiansong, J., Tiemin, W., Weibin, Y., Zufei, W.: Early CT Signs and Differential Diagnosis of COVID-19. Science Press (2020)

    Google Scholar 

  7. 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 

  8. Li, T., et al.: Nonlinear sinogram smoothing for low-dose X-ray CT. IEEE Trans. Nucl. Sci. 51(5), 2505–2513 (2004)

    Article  Google Scholar 

  9. D’Souza, K., Aras, M.: Applications of CAD/CAM technology in dental implant planning and implant surgery. In: Chaughule, R.S., Dashaputra, R. (eds.) Advances in Dental Implantology using Nanomaterials and Allied Technology Applications, pp. 247–286. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-52207-0_11

    Chapter  Google Scholar 

  10. Yinsheng, L., Garrett, J.W., Ke, L., Charles, S., Guang-Hong, C.: An enhanced smart-recon algorithm for time-resolved c-arm cone-beam ct imaging. IEEE Trans. Med. Imaging 39(6), 1894–1905 (2020)

    Article  Google Scholar 

  11. He, Q., Ma, L., You, C.: Letter by He et al regarding article, “signs of pulmonary infection on admission chest computed tomography are associated with pneumonia or death in patients with acute stroke”. Stroke, 51(11) (2020)

    Google Scholar 

  12. Buzug, T.M.: Computed Tomography: from Photon Statistics to Modern Cone-Beam CT. Springer, Leipzig (2008). https://doi.org/10.1007/978-3-540-39408-2

    Book  Google Scholar 

  13. Natterer, F.: The Mathematics of Computerized Tomography. Wiley, New York (1986)

    Book  Google Scholar 

  14. Sidky, E.Y., Pan, X.: Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization. Phys. Med. Biol. 53, 4777–4807 (2008)

    Article  Google Scholar 

  15. Frikel, J.: Sparse regularization in limited angle tomography. Appl. Comput. Harmon. Anal. 34(1), 117–141 (2013)

    Article  MathSciNet  Google Scholar 

  16. Frikel, J.: A new framework for sparse regularization in limited angle x-ray tomography. In: IEEE International Symposium on Biomedical Imaging: From Nano To Macro, pp. 824–827. IEEE Press, Piscataway (2010)

    Google Scholar 

  17. Li, Z., Jiqiang, G., Baodong, L.: Limited-angle cone-beam computed tomography image reconstruction by total variation minimization and piecewise-constant modifcation. J. Inverse Ill-Posed Probl. 21(6), 735–754 (2013)

    MathSciNet  MATH  Google Scholar 

  18. Frikel, J., Quinto, E.T.: Characterization and reduction of artifacts in limited angle tomography. Inverse Prob. 29(12) 125007 (2013)

    Google Scholar 

  19. Quinto, E.T.: Artifacts and visible singularities in limited data x-ray tomography. Sens. Imaging 18(1), 9 (2017)

    Article  Google Scholar 

  20. Sidky, E.Y., Kao, C., Pan, X.: Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT. J. Xray Sci. Technol. 14, 119–139 (2006)

    Google Scholar 

  21. Mumford, D., Shah, J.: Optimial approximation by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42, 577–685 (1989)

    Article  MathSciNet  Google Scholar 

  22. Cai, X., Chan, R., Zeng, T.: A two-stage image segmentation method using a convex variant of the Mumford-Shah model and thresholding. SIAM J. Imag. Sci. 6(1), 368–390 (2013)

    Article  MathSciNet  Google Scholar 

  23. Li, Z., Wang, C.: Error bounds and stability in the l0 regularized for CT reconstruction from small projections. Inverse Prob. Imaging 10(3), 829–853 (2017)

    MATH  Google Scholar 

  24. Boyer, C., et al.: Compressed sensing with structured sparsity and structured acquisition. Appl. Comput. Harmon. Anal. 46(2), 312–350 (2019)

    Article  MathSciNet  Google Scholar 

  25. Bin, D., Yong, Z.: An efficient algorithm for l0 minimization in wavelet frame based image restoration. J. Sci. Comput. 54(2–3), 350–368 (2013). https://doi.org/10.1007/s10915-012-9597-4

    Article  MathSciNet  MATH  Google Scholar 

  26. Bolte, J., Sabach, S., Teboulle, M.: Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math. Program. 146(1–2), 459–494 (2013). https://doi.org/10.1007/s10107-013-0701-9

    Article  MathSciNet  MATH  Google Scholar 

  27. Boyd, S.: Alternating direction method of multipliers (2011)

    Google Scholar 

  28. Gauss-Seidel Method (2010)

    Google Scholar 

  29. Wang, C., Luo, X., Wei, Y., Guo, Y., Zhang, L.: A variational proximal alternating linearized minimization in a given metric for limited-angle CT image reconstruction. Appl. Math. Modell. 67, 315–336 (2019)

    Article  MathSciNet  Google Scholar 

  30. Frankel, P., Garrigos, G., Peypouquet, J.: Splitting methods with variable metric for KL functions. J. Optim. Theory Appl. 165(3), 874–900 (2015)

    Article  MathSciNet  Google Scholar 

  31. Bredies, K.: Soft-thresholding. J. Fourier Anal. Appl. 14(5–6), 813–837 (2008)

    Article  MathSciNet  Google Scholar 

  32. Blumensath, T., Yaghoobi, M., Davies, M.E.: Iterative hard thresholding and L0 regularisation. In: IEEE International Conference on Acoustics. IEEE (2007)

    Google Scholar 

  33. Segars, W.P.: Development and application of the new dynamic NURBS-based cardiac-torso (NCAT) phantom. The University of North Carolina at Chapel Hill (2001)

    Google Scholar 

  34. Storath, M., Weinmann, A., Frikel, J., et al.: Joint image reconstruction and segmentation using the Potts model. Inverse Prob. 31(2), 25003–25031(29) (2014)

    Google Scholar 

  35. Chow, L.S., Paramesran, R.: Review of medical image quality assessment. Biomed. Signal Process. Control 27, 145–154 (2016)

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN2019013), the Scientific Research Foundation of Chongqing University of Arts and Sciences (Grant No. R2019FSC17), the Natural Science Foundation of Chongqing Municipal Science and Technology Commission (Grant numbers: cstc2020jcyj-msxm2352), and the Open Project of Key Laboratory No.CSSXKFKTQ202004, School of Mathematical Sciences, Chongqing Normal University.

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Authors and Affiliations

  1. Chongqing Key Laboratory of Group and Graph Theories and Applications, Chongqing University of Arts and Sciences, Chongqing, China

    Lingli Zhang, Huichuan Liang, Xiao Hu & Yi Xu

  2. Chongqing Key Laboratory of Complex Data Analysis and Artificial Intelligence, Chongqing University of Arts and Sciences, Chongqing, China

    Lingli Zhang, Huichuan Liang, Xiao Hu & Yi Xu

  3. Key Lab for OCME, Chongqing Normal University, Chongqing, China

    Lingli Zhang

  4. Engineering Research Center of Industrial Computed Tomography Nondestructive Testing of the Education Ministry of China, Chongqing University, Chongqing, China

    Lingli Zhang

Authors
  1. Lingli Zhang
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  2. Huichuan Liang
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  3. Xiao Hu
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  4. Yi Xu
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Corresponding author

Correspondence to Lingli Zhang .

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Editors and Affiliations

  1. Beijing Institute of Technology, Beijing, China

    Yongtian Wang

  2. Beijing Institute of Technology, Beijing, China

    Weitao Song

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Zhang, L., Liang, H., Hu, X., Xu, Y. (2021). A Regularized Limited-Angle CT Reconstruction Model Based on Sparse Multi-level Information Groups of the Images. In: Wang, Y., Song, W. (eds) Image and Graphics Technologies and Applications. IGTA 2021. Communications in Computer and Information Science, vol 1480. Springer, Singapore. https://doi.org/10.1007/978-981-16-7189-0_21

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  • DOI: https://doi.org/10.1007/978-981-16-7189-0_21

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  • Online ISBN: 978-981-16-7189-0

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