Geodesic
The central slice theorem generalization for a fan-beam tomography
Numerical methods and programming, Tome 7 (2006) no. 2, pp. 180-184

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The problems of few-view tomography require sophisticated iterative algorithms which employ a priori information on an unknown object. One of the well-developed algorithms for parallel tomography is the Gerchberg-Papoulis algorithm, which alternately iterates images in Fourier space and in image space. The application of this algorithm in the case of fan-beam tomography is blocked by the lack of the corresponding central slice theorem that connects 1D Fourier coefficients of projections with the Fourier coefficients of a 2D image. In this paper, we formulate the central slice theorem for the case of fan-beam tomography. The use of this modified theorem is illustrated by several numerical examples.
Keywords: central slice theorem, fan-beam tomography, iterative algorithms
Mots-clés : projective transformation, Gerchberg-Papoulis algorithm. 
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     title = {The central slice theorem generalization for a fan-beam tomography},
     journal = {Numerical methods and programming},
     pages = {180--184},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2006_7_2_a2/}
}
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V. V. Pickalov; D. I. Kazantsev; V. P. Golubyatnikov. The central slice theorem generalization for a fan-beam tomography. Numerical methods and programming, Tome 7 (2006) no. 2, pp. 180-184. http://geodesic.mathdoc.fr/item/VMP_2006_7_2_a2/