Early Results on General Vertex Sets and Truncated Projections in Cone-Beam Tomography
This paper summarizes a talk titled “Some recent results in cone-beam tomography” which was presented at the IMA workshop “Computational Radiology and Imaging: Therapy and Diagnostics” March 17–21, 1997.
A cone-beam projection of some object is a collection of rays-sums through the object where all the rays converge in a single “vertex point” in space.Usually this vertex point is outside the object and is often assumed that from each vertex-point, every non-zero ray-sum through the object is available.If some of these ray-sums are not available, the cone-beam projection is called a truncated projection.
Several algorithms are available to reconstruct the object from its cone-beam projections,under the assumptions that the vertex point travels along a suitable path in space and that no projection is truncated data will be discussed,and an algorithm that is able to reconstruct from a discrete,unordered set of vertex points (but with no truncated projections) will be presented.
Images obtained from these algorithms will be presented for the cases of computer -simulated data, and for data taken from a large-area CT scanner.
KeywordsSingle Photon Emission Compute Tomography Vertex Point Dynamic Single Photon Emission Compute Tomography Vertex Path Computational Radiology
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- R. Clack, M. Defrise, Overview of reconstruction algorithms for exact cone-beam tomography, SPIE Proceedings series, 2299, Mathematical Methods in Medical Imaging III, San Diego, CA, 1994Google Scholar
- P. Grangeat, Analyse d’un système d’imagerie 3D par reconstruction à partir de radiographies X en géométrie conique, Ph.D. Thesis, Ecole Nationale Supérieure des Télécommunications, France, 1987.Google Scholar
- P. Grangeat, Mathematical framework of cone-beam 3D reconstruction via the first derivative of the Radon transform, Mathematical methods in tomography, Herman, Louis and Natterer (eds.), Lecture Notes in Mathematics 1497, 66–97, Springer-Verlag, Berlin 1991.Google Scholar
- W. P. Klein, H. H. Barrett, I. W. Pang, D. D. Patton, M. M. Rogulski, J. D. Sain, FASTSPECT: Electrical and mechanical design of a high-resolution dynamic SPECT imager, Conference Record of the 1995 Nuclear Science Symposium and Medical Imaging Conference, San Francisco, CA, 931–933, 1996.Google Scholar
- H. Kudo, T. Saito, An extended completeness condition for exact cone-beam reconstruction and its application, IEEE Conference Record of the 1994 Nuclear Science Symposium and Medical Imaging Conference, Norfolk, VA., 1710–1714, 1995.Google Scholar
- F. Noo, R. Clack, M. Defrise, Cone-beam Reconstruction from General Discrete Vertex Sets, IEEE Conference Record of the 1996 Nuclear Science Symposium and Medical Imaging Conference, Anaheim, CA., 1496–1500, 1997.Google Scholar
- F. Noo, R. Clack, T. J. Roney, T. A. White, Symmetrical vertex paths for exact reconstruction in cone-beam C.T., Phys. Med. Biol., 43, 797–810, 1998.Google Scholar
- F. Noo, M. Defrise, R. Clack, T. J. Roney, T. A. White, S. G. Galbraith, Stable and Efficient Shift-Variant Algorithm for Circle-plus-Lines Orbits in Cone-Beam C.T., Proceedings ICIP-96: 1996 International Conference on Image Processing, Lausanne, September 1996, P. Delogne (ed). IEEE, Ceuterick, Leuven, Belgium, 539–542, 1996.Google Scholar
- T. J. Roney, S. G. Galbraith, T. A. White, M. O’reilly, R. Clack, M. DE-Frise, F. Noo, Feasibility and applications of cone-beam X-ray imaging for containerized waste, Proceedings for the 4th Nondestructive Assay and Nondestructive Examination Waste Characterization Conference (Salt Lake City, 1995, 295–324, 1995.Google Scholar
- Y. Weng, G. L. Zeng, G. T. Gullberg, A reconstruction algorithm for helical cone-beam SPECT, IEEE Trans. Nuc. Sci., 40, 1092–1101, 1993.Google Scholar