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An algorithm for 3D ultrasound tomography

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Book cover Inverse Problems of Wave Propagation and Diffraction

Part of the book series: Lecture Notes in Physics ((LNP,volume 486))

Abstract

Ultrasound tomography is modeled by the inverse problem of a 3D Helmholtz equation at fixed frequency with plane wave irradiation. It is assumed that the field is measured outside the support of the unknown potential f for finitely many incident waves. Starting out from an initial guess f0 for f we propagate the measured field through the object f0 to yield a computed field whose difference to the measurements is in turn backpropagated. The backpropagated field is used to update f0. The propagation as well as the backpropagation are done by a finite difference marching scheme. The whole process is carried out in a single step fashion, i.e. the updating is done immediately after backpropagating a single wave. It is very similar to the well known ART method in X-ray tomography, with the projection and backprojection step replaced by propagation and backpropagation. Numerical experiments with a 3D breast phantom on a 65×65×65 grid are presented.

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Authors and Affiliations

  1. Institut für Numerische und instrumentelle Mathematik, Westfälische Wilhelms-Universität, Einsteinstrasse 62, D-48149, Münster, Germany

    Frank Natterer

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  1. Frank Natterer
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Guy Chavent Pierre C. Sabatier

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© 1997 Springer-Verlag

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Natterer, F. (1997). An algorithm for 3D ultrasound tomography. In: Chavent, G., Sabatier, P.C. (eds) Inverse Problems of Wave Propagation and Diffraction. Lecture Notes in Physics, vol 486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105772

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  • DOI: https://doi.org/10.1007/BFb0105772

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62865-1

  • Online ISBN: 978-3-540-68713-9

  • eBook Packages: Springer Book Archive

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