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Ultrasonic Computed Tomography

  • Philippe LasayguesEmail author
  • Régine Guillermin
  • Jean-Pierre Lefebvre
Chapter

Abstract

Ultrasonic Computed Tomography (UCT) is a full digital imaging technique, which consists in numerically solving the inverse scattering problem associated to the forward scattering problem describing the interaction of ultrasonic waves with inhomogeneous media. For weakly inhomogeneous media such as soft tissues, various approximations of the solution of the forward problem (straight ray approximation, Born approximation, etc.), leading to easy-to-implement approximations of the inverse scattering problem (back-projection or back-propagation algorithms) can be used. In the case of highly heterogeneous media such as bone surrounded by soft tissues, such approximations are no more valid. We present here two non-linear inversion schemes based on high-order approximations. These methods are conceived like the prolongation of the methods implemented in the weakly inhomogeneous case for soft tissues. The results show the feasibility of this UCT approach to bones and its potential to perform measurements in vivo.

Keywords

Acoustical impedance Adult thighbone Algebraic inversion Artificial resin Back-projection Back-propagation Born approximation Childhood fibula Circular arrays Compound quantitative ultrasonic tomography Computed tomography Conjugated-gradient method Constant background Cortical bone Cross-sectional imaging Diffraction measurements Distorted Born diffraction tomography Electronic steering Far field asymptotic method Filtered back-projection algorithm Geometrically-mimicking phantom Green function High impedance contrast High-order approximations Integral equation Inverse problem Inverse scattering Iterative method Linear arrays Lippmann-Schwinger equation Low-contrasted tissues Lumbar vertebrae Mechanical scanning Mechanical steering Neukadur ProtoCast 113TM Non-linear inversion Osteoporosis Papoulis deconvolution Prototypes Reflection measurements Regularization process Resolution Scattered field Snell-Descartes laws Spatial Fourier transforms Toroidal arrays Transducers Transmission measurements Variable background Wave attenuation Wave velocity Wavelet analysis 

Notes

Acknowledgment

The authors are grateful for medical assistance from Dr P. Petit and Dr. J.-L. Jouve at Public Assistance Hospitals in Marseille and the “Timone” Children’s Hospital. The X-ray tomographies were performed by V. Kaftandjian at the Laboratory for Nondestructive Testing using Ionizing Radiation, INSA, Lyon.

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Copyright information

© Springer Netherlands 2011

Authors and Affiliations

  • Philippe Lasaygues
    • 1
    Email author
  • Régine Guillermin
    • 1
  • Jean-Pierre Lefebvre
    • 1
  1. 1.Laboratoire de Mécanique et d’AcoustiqueUPR CNRS 7051Marseille cedex 20France

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