DOI QR코드

DOI QR Code

Performance Comparison of Ray-Driven System Models in Model-Based Iterative Reconstruction for Transmission Computed Tomography

투과 컴퓨터 단층촬영을 위한 모델 기반 반복연산 재구성에서 투사선 구동 시스템 모델의 성능 비교

  • Jeong, J.E. (Department of Electronic Engineering, Paichai University) ;
  • Lee, S.J. (Department of Electronic Engineering, Paichai University)
  • Received : 2014.08.11
  • Accepted : 2014.10.07
  • Published : 2014.10.31

Abstract

The key to model-based iterative reconstruction (MBIR) algorithms for transmission computed tomography lies in the ability to accurately model the data formation process from the emitted photons produced in the transmission source to the measured photons at the detector. Therefore, accurately modeling the system matrix that accounts for the data formation process is a prerequisite for MBIR-based algorithms. In this work we compared quantitative performance of the three representative ray-driven methods for calculating the system matrix; the ray-tracing method (RTM), the distance-driven method (DDM), and the strip-area based method (SAM). We implemented the ordered-subsets separable surrogates (OS-SPS) algorithm using the three different models and performed simulation studies using a digital phantom. Our experimental results show that, in spite of the more advanced features in the SAM and DDM, the traditional RTM implemented in the OS-SPS algorithm with an edge-preserving regularizer out-performs the SAM and DDM in restoring complex edges in the underlying object. The performance of the RTM in smooth regions was also comparable to that of the SAM or DDM.

Keywords

References

  1. Gengsheng Lawrence Zeng, Medical Image Reconstruction: A conceptual Tutorial, Heidelberg, Dordrecht, London, New York, Springer, 2010.
  2. Jerrold T. Bushberg, J. Anthony Seibert, Edwin M. Leidholdt, John M. Boone, The Essential Physics of Medical Imaging, 2nd Ed,. LippincottWilliams & Wilkins, Philadelphia, PA, 2002.
  3. Thorsten M.Buzug, Computed Tomography From Photon Statistics to Modern Cone-Beam CT, Berlin, Heidelberg, Springer, 2008.
  4. J. Hsieh, B. Nett, Z. Yu, K. Sauer, J.-B, Thibault, C.Bouman, "Recent Advances in CT Image Reconstruction", Current Radiology Reports, vol. 1, no. 1, pp. 39-51, 2013. https://doi.org/10.1007/s40134-012-0003-7
  5. J. Thibault, K. Sauer, C. Bouman, J. Hsieh, "A three-dimensional statistical approach to improved image quality for multi-slice helical CT," Medical Physics, vol. 34, no. 11, pp. 4526-44, 2007. https://doi.org/10.1118/1.2789499
  6. F. Xu, K. Mueller, "Accelerating popular tomographic reconstruction algorithms on commodity PC graphics hardware," IEEE Trans. Nucl. Sci., vol. 52, pp. 654-663, 2005. https://doi.org/10.1109/TNS.2005.851398
  7. V.-G. Nguyen, S.-J. Lee, and M. N. Lee, "GPU-accelerated 3-D Bayesian image reconstruction from Compton scattered data," Phys. Med. Biol., vol. 56, no. 9, pp. 2817-2836, 2011. https://doi.org/10.1088/0031-9155/56/9/012
  8. V.-G. Nguyen and S.-J. Lee, "Graphics processing unit-accelerated iterative tomographic reconstruction with strip-integral system model," Opt. Eng., vol. 51, no. 9, pp. 093203:1-11, 2012.
  9. R. L. Siddon, "Fast calculation of the exact radiological path for a three-dimensional CT array," Med. Phys., vol. 12, no. 2, pp. 252-255, 1985. https://doi.org/10.1118/1.595715
  10. S. C. B. Lo, "Strip and line path integrals with a square pixel matrix: a unified theory for computational CT projections," IEEE Trans. Med. Imag., vol. 7, no. 4, pp. 355-363, 1988. https://doi.org/10.1109/42.14519
  11. B. De Man and S. Basu, "Distance-driven projection and backprojection in three dimensions," Phys. Med. Biol., vol. 49, pp. 2463-2475, 2004. https://doi.org/10.1088/0031-9155/49/11/024
  12. Y. Long, J. A. Fessler, and J. M. Balter, "3D forward and back-projection for X-ray CT using separable footprints," IEEE Trans. Med. Imag., vol. 29, no. 11, pp. 1839-1850, 2010. https://doi.org/10.1109/TMI.2010.2050898
  13. V.-G. Nguyen, S.-J. Lee, "Graphics Processing Unit-Accelerated Iterative Tomographic Reconstruction with Strip-Integral System Model," Opt. Eng., vol. 51, no. 9, pp. 093203:1-11, Sep. 2012.
  14. H. Erd gan, J. A. Fessler, "Ordered subsets algorithms for transmission tomography," Phys. Med. Biol., vol. 44, no. 11, pp. 2835-2851, 1999. https://doi.org/10.1088/0031-9155/44/11/311
  15. H. M. Hudson, R. S. Larkin, "Accelerated image reconstruction using ordered subsets of projection data," IEEE Trans. Med. Imag., vol. 13, no. 4, pp. 601-609, 1994. https://doi.org/10.1109/42.363108
  16. C. Kamphius and F. J. Beekman, "Accelerated Iterative Transmission CT Reconstruction Using An Ordered Subsets Convex Algorithm," IEEE Trans. Med. Imag., vol. 17, pp. 1001-1005, 1983.
  17. S.-J. Lee, "Accelerated Deterministic Annealing Algorithms for Transmission CT Reconstruction Using Ordered Subsets," IEEE Trans. Nucl. Sci., vol. 49, no. 5, pp. 2373-2380, Oct. 2002. https://doi.org/10.1109/TNS.2002.803869
  18. S.-J. Lee, "Performance comparison of convex-nonquadratic priors for Bayesian tomographic reconstruction," J. Electronic Imaging, vol. 9, no. 3, pp. 242-250, Jul. 2000. https://doi.org/10.1117/1.482752
  19. D. Kim, D. Pal, J.-B. Thibault, J. A. Fessler, "Accelerating ordered subsets image reconstruction for X-ray CT using spatially nonuniform optimization transfer," IEEE Trans. Med. Imag., vol. 32, no. 11, pp. 1965-1978, 2013. https://doi.org/10.1109/TMI.2013.2266898
  20. S. Geman, D. E. McClure, "Bayesian Image Analysis: An Application To Single Photon Emission Tomography," In Proc. Stat. Comp. Sect. of Amer. Stat. Assoc., pp. 12-18, 1985.
  21. H. Erdo gan, J. A. Fessler, "Monotonic algorithms for transmission tomography," IEEE Trans. Med. Imag., vol. 18, no. 9, pp. 801-814, 1999. https://doi.org/10.1109/42.802758
  22. P. J. Huber, Robust Statistics. New York: Wiley, 1981.
  23. K. Lange, "Convergence of EM image reconstruction algorithms with Gibbs smoothing," IEEE Trans. Med. Imag., vol. 9, no. 4, pp. 439-446, 1990. https://doi.org/10.1109/42.61759
  24. A. R. De Pierro, "On the Relation Between the ISRA and the EM Algorithm for Positron Emission Tomography," IEEE Trans. Med. Imag., vol. 12, no. 2, pp. 328-333, June 1993. https://doi.org/10.1109/42.232263
  25. A. R. De Pierro, "A Modied Expectation Maximization Algorithm for Penalized Likelihood Estimation in Emission Tomography," IEEE Trans. Med. Imag., vol. 14, no. 1, pp. 132-137, Mar. 1993.