A reconstruction approach for imaging in 3D cone beam vector field tomography

Authors:
T. Schuster;D. Theis;A. K. Louis
Affiliations:
Department of Mechanical Engineering, Helmut Schmidt University, Hamburg, Germany;Department of Applied Mathematics, Saarland University, Germany;Department of Applied Mathematics, Saarland University, Germany
Venue:
Journal of Biomedical Imaging
Year:
2008

Citing 3
Cited 1

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Direct algebraic reconstruction and optimal sampling in vectorfield tomography

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Tomographic Reconstruction of the Curl and Divergence of 2D Vector Fields Taking Refractions into Account

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Abstract

3D cone beam vector field tomography (VFT) aims for reconstructing and visualizing the velocity field of a moving fluid by measuring line integrals of projections of the vector field. The data are obtained by ultrasound measurements along a scanning curve which surrounds the object. From a mathematical point of view, we have to deal with the inversion of the vectorial cone beam transform. Since the vectorial cone beam transform of any gradient vector field with compact support is identically equal to zero, we can only hope to reconstruct the solenoidal part of an arbitrary vector field. In this paper we will at first summarize important properties of the cone beam transform for three-dimensional solenoidal vector fields and then propose a solution approach based on the method of approximate inverse. In this context, we intensively make use of results from scalar 3D computerized tomography. The findings presented in the paper will continuously be illustrated by pictures from first numerical experiments done with exact, simulated data.