Geodesic
Fast X-ray sum calculation algorithm for computed tomography problem
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 13 (2020) no. 1, pp. 95-106 Cet article a éte moissonné depuis la source Math-Net.Ru

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In iterative methods of computed tomography, each iteration requires to calculate a multitude of sums over values for the current reconstruction approximation. Each summable set is an approximation of a straight line in the three-dimensional space. In a cone-beam tomography, the number of sums to be calculated on each iteration has a cubic dependence on the linear size of the reconstructed image. Direct calculation of these sums requires the number of summations in a quartic dependence on the linear image size, which limits the performance of the iterative methods. The novel algorithm proposed in this paper approximates the three-dimensional straight lines using dyadic patterns, and, using the adjustment of precalculation and inference complexity similar to the adjustment employed in the Method of Four Russians, provides the calculation of these sums with a sub-quartic dependence on the linear size of the reconstructed image.
Keywords: computed tomography, fast Hough transform, Method of Four Russians.
Mots-clés : algebraic reconstruction, fast Radon transform 
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K. B. Bulatov; M. V. Chukalina; D. P. Nikolaev. Fast X-ray sum calculation algorithm for computed tomography problem. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 13 (2020) no. 1, pp. 95-106. http://geodesic.mathdoc.fr/item/VYURU_2020_13_1_a6/

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