A Multi-channel DART Algorithm

  • Mathé ZeegersEmail author
  • Felix Lucka
  • Kees Joost Batenburg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11255)


Tomography deals with the reconstruction of objects from their projections, acquired along a range of angles. Discrete tomography is concerned with objects that consist of a small number of materials, which makes it possible to compute accurate reconstructions from highly limited projection data. For cases where the allowed intensity values in the reconstruction are known a priori, the discrete algebraic reconstruction technique (DART) has shown to yield accurate reconstructions from few projections. However, a key limitation is that the benefit of DART diminishes as the number of different materials increases. Many tomographic imaging techniques can simultaneously record tomographic data at multiple channels, each corresponding to a different weighting of the materials in the object. Whenever projection data from more than one channel is available, this additional information can potentially be exploited by the reconstruction algorithm. In this paper we present Multi-Channel DART (MC-DART), which deals effectively with multi-channel data. This class of algorithms is a generalization of DART to multiple channels and combines the information for each separate channel-reconstruction in a multi-channel segmentation step. We demonstrate that in a range of simulation experiments, MC-DART is capable of producing more accurate reconstructions compared to single-channel DART.


Computed tomography Discrete tomography Discrete algebraic reconstruction technique (DART) Multi-channel segmentation 


  1. 1.
    van Aarle, W., Batenburg, K.J., Sijbers, J.: Automatic parameter estimation for the discrete algebraic reconstruction technique (DART). IEEE Trans. Image Process. 21(11), 4608–4621 (2012)MathSciNetCrossRefGoogle Scholar
  2. 2.
    van Aarle, W., et al.: Fast and flexible X-ray tomography using the ASTRA toolbox. Opt. Express 24(22), 25129–25147 (2016)CrossRefGoogle Scholar
  3. 3.
    Batenburg, K.J., Fortes, W., Hajdu, L., Tijdeman, R.: Bounds on the quality of reconstructed images in binary tomography. Discret. Appl. Math. 161(15), 2236–2251 (2013)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Batenburg, K.J., Sijbers, J.: DART: a fast heuristic algebraic reconstruction algorithm for discrete tomography. In: 2007 IEEE International Conference on Image Processing. ICIP 2007, vol. 4, pp. IV-133. IEEE (2007)Google Scholar
  5. 5.
    Batenburg, K.J., Sijbers, J.: DART: a practical reconstruction algorithm for discrete tomography. IEEE Trans. Image Process. 20(9), 2542–2553 (2011)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Bleichrodt, F., Tabak, F., Batenburg, K.J.: SDART: an algorithm for discrete tomography from noisy projections. Comput. Vis. Image Underst. 129, 63–74 (2014)CrossRefGoogle Scholar
  7. 7.
    Buzug, T.M.: Computed Tomography: From Photon Statistics to Modern Cone-Beam CT. Springer, Heidelberg (2008). Scholar
  8. 8.
    Dabravolski, A., Batenburg, K.J., Sijbers, J.: A multiresolution approach to discrete tomography using DART. PloS one 9(9), e106090 (2014)CrossRefGoogle Scholar
  9. 9.
    Frank, J.: Electron Tomography. Springer, New York (1992). Scholar
  10. 10.
    Hsieh, J., et al.: Computed Tomography: Principles, Design, Artifacts, and Recent Advances. SPIE, Bellingham (2009)Google Scholar
  11. 11.
    Kak, A.C., Slaney, M., Wang, G.: Principles of computerized tomographic imaging. Med. Phys. 29(1), 107–107 (2002)CrossRefGoogle Scholar
  12. 12.
    Kazantsev, D., Jørgensen, J.S., Andersen, M.S., Lionheart, W.R., Lee, P.D., Withers, P.J.: Joint image reconstruction method with correlative multi-channel prior for X-ray spectral computed tomography. Inverse Probl. 34(6), 064001 (2018)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Maestre-Deusto, F.J., Scavello, G., Pizarro, J., Galindo, P.L.: Adart: an adaptive algebraic reconstruction algorithm for discrete tomography. IEEE Trans. Image Process. 20(8), 2146–2152 (2011)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Midgley, P., Weyland, M.: 3D electron microscopy in the physical sciences: the development of Z-contrast and EFTEM tomography. Ultramicroscopy 96(3–4), 413–431 (2003)CrossRefGoogle Scholar
  15. 15.
    Palenstijn, W.J., Batenburg, K.J., Sijbers, J.: The ASTRA tomography toolbox. In: 13th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE, vol. 2013, pp. 1139–1145 (2013)Google Scholar
  16. 16.
    Tairi, S., Anthoine, S., Morel, C., Boursier, Y.: Simultaneous reconstruction and separation in a spectral CT framework. In: Nuclear Science Symposium, Medical Imaging Conference and Room-Temperature Semiconductor Detector Workshop (NSS/MIC/RTSD), 2016, pp. 1–4. IEEE (2016)Google Scholar
  17. 17.
    Wilson, M., et al.: A 10 cm \(\times \) 10 cm CdTe spectroscopic imaging detector based on the HEXITEC ASIC. J. Instrum. 10(10), P10011 (2015)CrossRefGoogle Scholar
  18. 18.
    Zhuge, X., Palenstijn, W.J., Batenburg, K.J.: TVR-DART: a more robust algorithm for discrete tomography from limited projection data with automated gray value estimation. IEEE Trans. Image Process. 25(1), 455–468 (2016)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Mathé Zeegers
    • 1
    Email author
  • Felix Lucka
    • 1
    • 2
  • Kees Joost Batenburg
    • 1
  1. 1.Computational ImagingCentrum Wiskunde & Informatica (CWI)AmsterdamThe Netherlands
  2. 2.Department of Computer ScienceUniversity College LondonLondonUK

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