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International Conference on Image Analysis and Recognition

ICIAR 2016: Image Analysis and Recognition pp 672–677Cite as

Sparse-View CT Reconstruction Using Curvelet and TV-Based Regularization

Part of the Lecture Notes in Computer Science book series (LNIP,volume 9730)

Abstract

The reconstruction from sparse-view projections is one of important problems in computed tomography limited by the availability or feasibility of a large number of projections. Total variation (TV) approaches have been introduced to improve the reconstruction quality by smoothing the variation between neighboring pixels. However, the TV-based methods for images with textures or complex shapes may generate artifacts and cause loss of details. Here, we propose a new regularization model for CT reconstruction by combining regularization methods based on TV and the curvelet transform. Combining curvelet regularizer, which is optimally sparse with better directional sensitivity than wavelet transforms with TV on the other hand will give us a unique regularization model that leads to the improvement of the reconstruction quality. The split-Bregman (augmented Lagrangian) approach has been used as a solver which makes it easy to incorporate multiple regularization terms including the one based on the multiresolution transformation, in our case curvelet transform, into optimization framework. We compare our method with the methods using only TV, wavelet, and curvelet as the regularization terms on the test phantom images. The results show that there are benefits in using the proposed combined curvelet and TV regularizer in the sparse view CT reconstruction.

Keywords

  • Computed tomography
  • Sparse-view reconstruction
  • Curvelet
  • Total variation

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References

  1. Brenner, D.J.J., Hall, E.J.: Computed tomography: an increasing source of radiation exposure. N. Engl. J. Med. 357(22), 2277–2284 (2007)

    CrossRef  Google Scholar 

  2. Oliveira, J.P., Bioucas-Dias, J.M., Figueiredo, M.A.T.: Adaptative total variation image deblurring: a majorization-minimization approach. Sig. Process. 89, 1683–1693 (2009)

    CrossRef  MATH  Google Scholar 

  3. Beck, A., Teboulle, M.: Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans. Image Process. 18(11), 2419–2434 (2009)

    CrossRef  MathSciNet  Google Scholar 

  4. Sidky, E.Y., Pan, X.: Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization. Phys. Med. Biol. 53(17), 4777–4807 (2008)

    CrossRef  Google Scholar 

  5. Herman, G.T., Davidi, R.: On image reconstruction from a small number of projections. Inv. Probl. 24(4), 45011–45028 (2008)

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Yang, J., Yu, H., Jiang, M., Wang, G.: High-order total variation minimization for interior tomography. Inv. Probl. 26(3), 035013 (2010)

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Starck, J.L., Candes, E.J., Donoho, D.L.: The curvelet transform for image denoising. IEEE Trans. Image Process. 11(6), 670–684 (2002)

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Tai, X.C., Wu, C.: Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model. In: Tai, X.-C., Mørken, K., Lysaker, M., Lie, K.-A. (eds.) Scale Space Variational Methods in Computer Vision. LNCS, vol. 5567, pp. 502–513. Springer, Berlin (2009)

    CrossRef  Google Scholar 

  9. Goldstein, T., Osher, S.: The split Bregman method for L1 regular-ized problems. SIAM J. Imaging Sci. 2(2), 323–343 (2009)

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Aelterman, J., Luong, H.Q., Goossens, B., Piurica, A., Philips, W.: Augmented Lagrangian based reconstruction of non-uniformly sub-Nyquist sampled MRI data. Sig. Process. 91(12), 2731–2742 (2011)

    CrossRef  Google Scholar 

  11. Vandeghinste, B., Goossens, B., Holen, R.V., Vanhove, C., Pizurica, A., Vandenberghe, S., Staelens, S.: Iterative CT reconstruction using shearlet-based regularization. IEEE Trans. Nucl. Sci. 60(5), 3305–3317 (2013)

    CrossRef  Google Scholar 

  12. Afonso, M.V., Bioucas-Dias, J.M., Figueiredo, M.A.T.: An augmented lagrangian approach to the constrained optimization formulation of imaging inverse problems. IEEE Trans. Image Process. 20(3), 681–695 (2011)

    CrossRef  MathSciNet  Google Scholar 

  13. Wu, H., Maier, A., Hornegger, J.: Iterative CT reconstruction using curvelet-based regularization. In: Meinzer, H.-P., Deserno, T.M., Handels, H., Tolxdorff, T. (eds.) Bildverarbeitung für die Medizin. Springer, Heidelberg (2013)

    Google Scholar 

  14. Hestenes, M.R., Stiefel, E.: Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bureau Stand. 49(6), 409–436 (1952)

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Shepp, L.A., Logan, B.F.: Reconstructing interior head tissue from X-ray transmissions. IEEE Trans. Nucl. Sci. 21(1), 228–236 (1974)

    CrossRef  Google Scholar 

  16. FORBILD group. http://www.imp.uni-erlangen.de/phantoms/head/head.html

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Acknowledgments

This work was supported by NASA EPSCoR under cooperative agreement No. NNX10AR89A.

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Authors and Affiliations

  1. Electrical and Computer Engineering Department, University of Nevada, Las Vegas, 89154, USA

    Ali Pour Yazdanpanah & Emma E. Regentova

Authors
  1. Ali Pour Yazdanpanah
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  2. Emma E. Regentova
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Corresponding author

Correspondence to Ali Pour Yazdanpanah .

Editor information

Editors and Affiliations

  1. University of Porto, Porto, Portugal

    Aurélio Campilho

  2. Department of Electrical, University of Waterloo, Waterloo, Ontario, Canada

    Fakhri Karray

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Yazdanpanah, A.P., Regentova, E.E. (2016). Sparse-View CT Reconstruction Using Curvelet and TV-Based Regularization. In: Campilho, A., Karray, F. (eds) Image Analysis and Recognition. ICIAR 2016. Lecture Notes in Computer Science(), vol 9730. Springer, Cham. https://doi.org/10.1007/978-3-319-41501-7_75

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  • DOI: https://doi.org/10.1007/978-3-319-41501-7_75

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-41500-0

  • Online ISBN: 978-3-319-41501-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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