Data Integral Invariant Based Beam-hardening Correction: A Simulation Study

Shaojie Tang, Kuidong Huang, Yunyong Cheng, Xuanqin Mou, Xiangyang Tang


Published in:Fully3D 2017 Proceedings


CT, beam-hardening, consistency condition, integral invariant
In computed tomography (CT), the polychromatic characteristics of x-ray photons emitting from source and absorbed by detector lead to beam-hardening effects in signal detection and image formation, especially in situations where a highly attenuating object (e.g., bone or metal in-plant) is in x-ray beam. Usually, the method called bone bam-hardening correction is employed to suppress the beam-hardening effects, in which either a scaling factor or a vector needs to be pre-determined via tedious physical experiments. Based on the Helgasson-Ludwig consistency condition (HLCC), a data consistency condition based beam-hardening correction has been proposed to avoid such a tedious parameter determination. However, the HLCC requires the involvement of neighboring projection views acquired at a relatively uniform and sufficient sampling rate, which hinders its application in the case wherein the sampling in view is sparse. Having recognized the flexibility of data integral invariant (DII), we extend the HLCC-based method by proposing a DII based objective function in this work. Using computer-simulated projection data, we carry out a simulation study to demonstrate that the process of parameter optimization and performance of the proposed beam-hardening correction method.
Shaojie Tang
School of Automation, Xi'an University of Posts and Telecommunications, Xi'an, Shaanxi 710121, China
Kuidong Huang
Key Lab of Contemporary Design and Integrated Manufacturing Technology (Northwestern Polytechnical University), Ministry of Education, Xi'an, Shaanxi 710072, China
Yunyong Cheng
Key Lab of Contemporary Design and Integrated Manufacturing Technology (Northwestern Polytechnical University), Ministry of Education, Xi'an, Shaanxi 710072, China
Xuanqin Mou
Institute of Image Processing and Pattern Recognition, Xi'an Jiaotong Univ., Xi'an, Shaanxi 710049, China
Xiangyang Tang
Department of Radiology and Imaging Sciences, Emory University School of Medicine, Atlanta, GA 30322, USA.
  1. W. D. McDavid, R. G. Waggener, W. H. Payne, and M. J. Dennis, “Correction for spectral artifacts in cross-sectional reconstruction for X-rays,” Med. Phys. 4, 54-57 (1977).
  2. G. T. Herman, “Correction for beam hardening in computed tomography,” Phys. Med. Biol. 24, 81-106 (1979).
  3. P. Joseph and R. Spital, “A method for correcting bone induced artifacts in computed tomography scanners,” J. Comput. Assist. Tomo. 2, 100-108 (1978).
  4. O. Nalcioglu and R. Y. Lou, “Post-reconstruction method for beam hardening in computerised tomography,” Phys. Med. Biol. 24, 330-340 (1979).
  5. B. De Man, J. Nuyts, P. Dupont, G. Marchal, and P. Suetens, “Metal streak artifacts in x-ray computed tomography: a simulation study,” IEEE Trans. Nucl. Sci. 46, 691-696 (1999).
  6. S. Tang, H. Yu, H. Yan, D. Bharkhada, and X. Mou, “X-ray projection simulation based on physical imaging model,” J. X-ray Sci. Tech. 14,177-189 (2006).
  7. S. Tang, X. Mou, Y. Yang, Q. Xu, and H. Yu, “Application of projection simulation based on physical imaging model to the evaluation of beam hardening corrections in X-ray transmission tomography,” J. X-ray Sci. Tech. 16, 95-117 (2008).
  8. F. Natterer, “The Mathematics of Computerized Tomography,” John Wiley & Sons Ltd, (1986).
  9. M. Li and D. Wang, “CT image reconstruction from limited information,” Proc. SPIE 2390, 116-126 (1995).
  10. S. Basu and Y. Bresler, “Uniqueness of tomography with unknown view angles,” IEEE Trans. Image Process. 9, 1094-1106 (2000).
  11. T. J. Wang and T. W. Sze, “The image moment method for the limited range CT image reconstruction and pattern recognition,” Pattern Recognition 34, 2145-2154 (2001).
  12. H. Yu, Y. Wei, J. Hsieh, and G. Wang, “Data consistency based translational motion artifact reduction in fan-beam CT,” IEEE Trans. Med. Imaging 25, 792-803 (2006).
  13. H. Yu and G. Wang, “Data consistency based rigid motion artifact reduction in fan-beam CT,” IEEE Trans. Med. Imaging 26, 249-260 (2007).
  14. J. Xu, K. Taguchi, and B. M. W. Tsui, “Statistical projection completion in x-ray CT using consistency conditions,” IEEE Trans. Med. Imaging 29, 1528-1540 (2010).
  15. Y. Wei, H. Yu, and G. Wang, “Integral Invariants for Computed Tomography,” IEEE Signal Processing Letters 13, 549-552 (2006).
  16. H. Yu and G. Wang, “Compressed sensing based interior tomography,” Phys. Med. Biol. 54, 2791-2805 (2009).
  17. G. Lauritsch and H. Bruder, “head phantom,”, (1998).
  18. T. R. Fewell, R. E. Shuping, and K. R. Hawkins, “Handbook of computed tomography x-ray spectra,” Washington, D.C.: HHS Publication (FDA) 81-8162, 27-29 (1981).
  19. J. A. Rowlands and K. W. Taylor, “Absorption and noise in cesium iodidex-ray image intensifiers,” Med. Phys. 10, 786-795 (1983).
  20. M. Kachelrieß, K. Sourbelle, and W. A. Kalender, “Empirical cupping correction: A first-order raw data precorrection for cone-beam computed tomography,” Med. Phys. 33, 1269-1273 (2006).
  21. Y. Kyriakou, E. Meyer, D. Prell, and M. Kachelrieß, “Empirical beam hardening correction (EBHC) for CT,” Med. Phys. 37, 5179-5187 (2010).
  22. G. Chen and S. Leng, “A new data consistency condition for fan-beam projection data,” Med. Phys. 32, 961-967 (2005).
  23. S. Leng, B. Nett, M. Speidel, and G. Chen, “Motion artifact reduction in fan-beam and cone-beam computed tomography via the Fan-beam Data Consistency Condition (FDCC),” Proc. SPIE 6510, 65101W (2007).
  24. F. John, “The ultrahyperbolic equation with four independent variables,”J. Duke Math. 4, 300-322 (1938)
  25. S. K. Patch, “Computation of Unmeasured Third-Generation VCT Views From Measured Views,” IEEE Trans. Med. Imaging 21, 801-813 (2002).
  26. S. K. Patch, “Consistency conditions upon 3D CT data and the wave equation,” Phys. Med. Biol. 47, 1-14 (2002).
  27. M. Defrise, F. Noo, and H. Kudo, “Improved two-dimensional rebinning of helical cone-beam computerized tomography data using John’s equation,” Inverse Probl. 19, S41-S54 (2003).
  28. S. Tang, Q. Xu, X. Mou, and X. Tang, “The mathematical equivalence of consistency conditions in the divergent-beam computed tomography,” Journal of X-Ray Science and Technology 20, 45-68 (2012). 
  29. S. Tang, X. Mou, Q. Xu, Y. Zhang, J. Bennett, and H. Yu, “Data consistency condition–based beam-hardening correction,” Optical Engineering 50, 076501 (2011).