A Reconstruction Approach for Imaging in 3D Cone Beam Vector Field Tomography
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 mathemati...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | International Journal of Biomedical Imaging |
| Online Access: | http://dx.doi.org/10.1155/2008/174283 |
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| author | T. Schuster D. Theis A. K. Louis |
| author_facet | T. Schuster D. Theis A. K. Louis |
| author_sort | T. Schuster |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a811624a80c94ae0b971b4f31664dd5c |
| institution | Kabale University |
| issn | 1687-4188 1687-4196 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Biomedical Imaging |
| spelling | doaj-art-a811624a80c94ae0b971b4f31664dd5c2025-02-03T01:21:15ZengWileyInternational Journal of Biomedical Imaging1687-41881687-41962008-01-01200810.1155/2008/174283174283A Reconstruction Approach for Imaging in 3D Cone Beam Vector Field TomographyT. Schuster0D. Theis1A. K. Louis2Department of Mechanical Engineering, Helmut Schmidt University, Holstenhofweg 85, 22043 Hamburg, GermanyDepartment of Applied Mathematics, Saarland University, P.O. Box 15 11 50, 66041 Saarbrücken, GermanyDepartment of Applied Mathematics, Saarland University, P.O. Box 15 11 50, 66041 Saarbrücken, Germany3D 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.http://dx.doi.org/10.1155/2008/174283 |
| spellingShingle | T. Schuster D. Theis A. K. Louis A Reconstruction Approach for Imaging in 3D Cone Beam Vector Field Tomography International Journal of Biomedical Imaging |
| title | A Reconstruction Approach for Imaging in 3D Cone Beam Vector Field Tomography |
| title_full | A Reconstruction Approach for Imaging in 3D Cone Beam Vector Field Tomography |
| title_fullStr | A Reconstruction Approach for Imaging in 3D Cone Beam Vector Field Tomography |
| title_full_unstemmed | A Reconstruction Approach for Imaging in 3D Cone Beam Vector Field Tomography |
| title_short | A Reconstruction Approach for Imaging in 3D Cone Beam Vector Field Tomography |
| title_sort | reconstruction approach for imaging in 3d cone beam vector field tomography |
| url | http://dx.doi.org/10.1155/2008/174283 |
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