Design criteria for geometrical calibration phantoms in fan and cone beam CT systems
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Peter Jonas
Abstract
Image quality in tomographic applications depends strongly on the precise knowledge of the geometrical parameters of x-ray source and detector. However, in some situations these geometrical data are not immediately available. One way to overcome this problem is to use calibration phantoms which consist of several opaque markers in a known geometry. A main question is what properties are needed in order to reliably determine the searched for geometry data. In this paper we give sufficient conditions for the calibration phantom such that the reconstruction problem has a unique solution. We also use our theoretical approach to derive a numerical method which can determine the needed geometry data. Our analyses show that this numerical method is stable and that the solutions are as good as those of standard nonlinear procedures like Gauss–Newton-type methods. Furthermore, our new algorithm is much faster than standard methods and it also does not depend on initial values.
References
[1] Y. Cho, D. J. Moseley and J. H. Siewedsen, Accurate technique for complete geometric calibration of cone-beam computed tomography systems, Med. Phys. 32 (2005), no. 4, 968–983. 10.1118/1.1869652Search in Google Scholar PubMed
[2] M. Gerrucci, R. K. Leach and C. Giusca, Towards geometrical calibration of x-ray computed tomography systems – A review, Meas. Sci. Technol. 26 (2015), 10.1088/0957-0233/26/9/092003/meta. 10.1088/0957-0233/26/9/092003/metaSearch in Google Scholar
[3] D. Gross and U. Heil, Auto calibration of cone-beam-CT, Med. Phys. 39 (2012), no. 10, 5959–5970. 10.1118/1.4739247Search in Google Scholar PubMed
[4] G. T. Gullberg, B. M. W. Tsui and C. R. Crawford, Estimation of geometrical parameters for fan beam tomography, Phys. Med. Biol. 32 (1987), no. 12, 1582–1594. 10.1088/0031-9155/32/12/005Search in Google Scholar
[5] J. Hess, P. Kuehnlein, S. Oeckl and T. Schoen, An acquisition geometry-independent calibration tool for industrial computed tomography, 4th International Symposium on NDT in Areospace, Allen Institute, Seattle (2012). Search in Google Scholar
[6] C. Mennessier and R. Clackdoyle, A simple analytic method for cone beam calibration, 2005 IEEE Nuclear Science Symposium Conference Record, IEEE Press, Piscataway (2005), 2743–2746. 10.1109/NSSMIC.2005.1596904Search in Google Scholar
[7] C. Mennessier, R. Clackdoyle and F. Noo, Direct determination of geometric alignment parameters for cone-beam scanners, Phys. Med. Biol. 54 (2009), no. 6, 1633–1660. 10.1088/0031-9155/54/6/016Search in Google Scholar PubMed PubMed Central
[8] F. Noo, R. Clackdoyle, C. Mennessier and T. A. White, Analytic method based on identification of ellipse parameters for scanner calibration in cone-beam tomography, Phy. Med. Biol. 45 (2000), no. 11, 3489–3508. 10.1088/0031-9155/45/11/327Search in Google Scholar PubMed
[9] N. Robert, K. N. Watt and X. Wang, The geometric calibration of cone-beam systems with arbitrary geometry, Phys. Med. Biol. 54 (2009), 7329–7261. 10.1088/0031-9155/54/24/001Search in Google Scholar PubMed
[10] F. Stopp, A. J. Wieckowski and M. Kaeseberg, A geometric calibration method for an open cone-beam CT system, 12th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, Fraunhofer IPK, Berlin (2013), 106–109. Search in Google Scholar
[11] Y. Sun, Y. Hou, F. Zaho and J. Hu, A calibration method for misaligned scanner geometry in cone-beam computed tomography, NDT & E Int. 39 (2006), no. 6, 499–513. 10.1016/j.ndteint.2006.03.002Search in Google Scholar
[12] K. Yang, A. L. C. Kwan, D. F. Miller and J. M. Boone, A geometric calibration method for cone beam CT systems, Med. Phys. 33 (2006), no. 6, 1695–1706. 10.1118/1.2198187Search in Google Scholar PubMed PubMed Central
[13] Y. Yang, L. Li and Z.-Q. Chen, A review of geometric calibration for different 3D-X-ray imaging systems, Nucl. Sci. Tech. 27 (2016), 10.1007/s41365-016-0073-y. 10.1007/s41365-016-0073-ySearch in Google Scholar
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Articles in the same Issue
- Frontmatter
- TGV-based multiplicative noise removal approach: Models and algorithms
- Design criteria for geometrical calibration phantoms in fan and cone beam CT systems
- Under-relaxed quasi-Newton acceleration for an inverse fixed-point problem coming from Positron Emission Tomography
- An adaptive iteration reconstruction method for limited-angle CT image reconstruction
- Accuracy estimates of regularization methods and conditional well-posedness of nonlinear optimization problems
- A non-smooth and non-convex regularization method for limited-angle CT image reconstruction
- Optimization analysis of the inverse coefficient problem for the nonlinear convection-diffusion-reaction equation
- A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation
- A numerical algorithm for constructing an individual mathematical model of HIV dynamics at cellular level
