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JOURNALS // Numerical methods and programming // Archive

Num. Meth. Prog., 2006 Volume 7, Issue 2, Pages 180–184 (Mi vmp590)

This article is cited in 1 paper

Вычислительные методы и приложения

The central slice theorem generalization for a fan-beam tomography

V. V. Pickalova, D. I. Kazantseva, V. P. Golubyatnikovb

a Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: 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, projective transformation, iterative algorithms, Gerchberg-Papoulis algorithm.

UDC: 519.633.9



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