Advertisement

Exponential vector field tomography

  • Kent Stråhlén
Session 10: Recognition & Reconstruction
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1311)

Abstract

In the exponential Radon transform in R2, the integrals of a scalar function f over lines, with exponential weight functions, are determined. In this paper we demonstrate how to define two different kinds of exponential Radon transforms for vector fields in R2 in a natural way. It is shown that having data from these transforms it is possible to reconstruct the vector field uniquely.

The motivation to study this problem is ultrasound measurements of flows, from which velocity spectra along lines can be determined. The first moment of these can be interpreted by means of one of the exponential vectorial Radon transforms.

Keywords

Vector Field Filter Back Projection Tomographic Reconstruction Velocity Spectrum Straight Pipe 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    H. Braun and A. Hauk. Tomographic reconstruction of vector fields. IEEE Transactions on signal processing, 39(2):464–471, 1991.CrossRefGoogle Scholar
  2. 2.
    T. Jansson, M. Almqvist, K. Stråhlén, R. Eriksson, G. Sparr, H. W. Persson, and K. Lindström. Ultrasound Doppler vector tomography — measurements of directional blood flow. Ultrasound in medicine and biology, 23(1):47–57, 1997.CrossRefPubMedGoogle Scholar
  3. 3.
    P. Juhlin. Principles of Doppler tomography. Technical report, Dept. of Mathematics, Lund Institute of Technology, 1992.Google Scholar
  4. 4.
    F. Natterer. The Mathematics of Computerized Tomography. John Wiley & Sons, Chichester, Mew York, Brisbane, Toronto, Singapore, 1986.Google Scholar
  5. 5.
    S. J. Norton. Unique tomographic reconstruction of vector fields using boundary data. IEEE Transactions on image processing, 1(3):406–412, 1992.CrossRefGoogle Scholar
  6. 6.
    J. L. Prince. Tomographic reconstruction of 3-d vector fields using inner product probes. IEEE Transactions on Image Processing, 3(2):216–219, March 1995.CrossRefGoogle Scholar
  7. 7.
    G. Sparr, K. Stråhlén, K. Lindström, and H. W. Persson. Doppler tomography for vector fields. Inverse Problems, 11:1051–1061, 1995.CrossRefGoogle Scholar
  8. 8.
    K. Stråhlén. Reconstructions from Doppler Radon transforms. In Proceedings of ICIP'96. IEEE, 1996.Google Scholar
  9. 9.
    K. Stråhlén, G. Sparr, M. Almqvist, and H. W. Persson. Ultrasound Doppler measurements of blood flows using tomographic methods. In Proceedings: BIOSIGNAL'96, 1996.Google Scholar
  10. 10.
    K. Stråhlén. Some Integral Transforms of Vector Fields. Licentiate thesis, Dept. of Mathematics, Lund Institute of Technology, Lund University, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Kent Stråhlén
    • 1
  1. 1.Department of MathematicsLund Institute of TechnologyLundSweden

Personalised recommendations