Sensing and Imaging

, 18:10 | Cite as

Motion Estimation and Compensation Strategies in Dynamic Computerized Tomography

Original Paper
  • 135 Downloads
Part of the following topical collections:
  1. Recent Developments in Sensing and Imaging

Abstract

A main challenge in computerized tomography consists in imaging moving objects. Temporal changes during the measuring process lead to inconsistent data sets, and applying standard reconstruction techniques causes motion artefacts which can severely impose a reliable diagnostics. Therefore, novel reconstruction techniques are required which compensate for the dynamic behavior. This article builds on recent results from a microlocal analysis of the dynamic setting, which enable us to formulate efficient analytic motion compensation algorithms for contour extraction. Since these methods require information about the dynamic behavior, we further introduce a motion estimation approach which determines parameters of affine and certain non-affine deformations directly from measured motion-corrupted Radon-data. Our methods are illustrated with numerical examples for both types of motion.

Keywords

Computerized tomography Radon transform Time-dependent inverse problems Feature extraction Motion estimation 

Mathematics Subject Classification

MSC 44A12 65R32 92C55 94A12 

References

  1. 1.
    Desbat, L., Roux, S., & Grangeat, P. (2007). Compensation of some time dependent deformations in tomography. IEEE Transaction on Medical Imaging, 26, 261–269.CrossRefMATHGoogle Scholar
  2. 2.
    Gravier, E., Yang, Y., & Jin, M. (2007). Tomographic reconstruction of dynamic cardiac image sequences. IEEE Transactions on Image Processing, 16, 932–942.MathSciNetCrossRefGoogle Scholar
  3. 3.
    Hahn, B. (2014). Reconstruction of dynamic objects with affine deformations in dynamic computerized tomography. Journal of Inverse Ill-Posed Problems, 22, 323–339.MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Hahn, B. N. (2014). Efficient algorithms for linear dynamic inverse problems with known motion. Inverse Problems, 30, 035008.MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Hahn, B. N., & Quinto, E. T. (2016). Detectable singularities from dynamic Radon data. SIAM Journal Imaging Sciences, 9, 1195–1225.MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Hörmander, L. (2003). The analysis of linear partial differential operators. I. Distribution theory and Fourier analysis, classics in mathematics. Berlin: Springer.MATHGoogle Scholar
  7. 7.
    Isola, A. A., Ziegler, A., Koehler, T., Niessen, W. J., & Grass, M. (2008). Motion-compensated iterative cone-beam CT image reconstruction with adapted blobs as basis functions. Physics in Medicine Biology, 53, 6777.CrossRefGoogle Scholar
  8. 8.
    Katsevich, A. (2010). An accurate approximate algorithm for motion compensation in two-dimensional tomography. Inverse Problems, 26, 065007.MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Katsevich, A., Silver, M., & Zamayatin, A. (2011). Local tomography and the motion estimation problem. SIAM Journal on Imaging Science, 4, 200–219.MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Krishnan, V. P., & Quinto, E. T. (2015). Microlocal analysis in tomography. In O. Scherzer (Ed.), Handbook of mathematical methods in imaging. New York: springer.Google Scholar
  11. 11.
    Louis, A. K. (1996). Approximate inverse for linear and some nonlinear problems. Inverse Problems, 12, 175.MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Louis, A. K. (2011). Feature reconstruction in inverse problems. Inverse Problems, 27, 065010.MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Lu, W., & Mackie, T. R. (2002). Tomographic motion detection and correction directly in sinogram space. Physics in Medicine and Biology, 47, 1267.CrossRefGoogle Scholar
  14. 14.
    Natterer, F. (1986). The mathematics of computerized tomography. chichester: Wiley.MATHGoogle Scholar
  15. 15.
    Ritchie, C. J., Hsieh, J., Gard, M. F., Godwin, J. D., Kim, Y., & Crawford, C. R. (1994). Predictive respiratory gating: A new method to reduce motion artifacts on CT scans. Radiology, 190, 847–852.CrossRefGoogle Scholar
  16. 16.
    Trèves, F. (1980). Introduction to pseudodifferential and Fourier integral operators, Vol. 1. Pseudodifferential operators. New York: The University Series in Mathematics Plenum Press.CrossRefMATHGoogle Scholar
  17. 17.
    Van Eyndhoven, G., Sijbers, J., & Batenburg, J. (2012). Combined motion estimation and reconstruction in tomography. Lecture Notes in Computer Science, 7583, 12–21.CrossRefGoogle Scholar
  18. 18.
    Yu, H., & Wang, G. (2007). Data consistency based rigid motion artifact reduction in fan-beam CT. IEEE Transactions on Medical Imaging, 26, 249–260.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WürzburgWürzburgGermany

Personalised recommendations