A New Fast Algorithm for Exact Calculation of the Discrete 2-D and 3-D X-Ray Transform

机译：精确计算离散2-D和3-D X射线变换的新快速算法

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A new algorithm for fast calculation of line integrals is proposed. The algorithm is applicable for both 2-D and 3-D digital data. We focus our discussion in the case of line integration over 3-D voxel arrays where speed is much more crucial than in the 2-D case. The fundamental idea is simultaneous calculation of a 2D array of line integrals using serial memory access in order to significantly reduce the computational cost. We compare our algorithm to the Fast Slant-Stack algorithm with respect to computation time and accuracy.

机译：提出了一种快速计算线积分的新算法。该算法适用于2D和3D数字数据。我们将讨论重点放在3D体素阵列上的线集成的情况下，在3D体素阵列上，速度比2D情况下更为重要。基本思想是使用串行存储器访问来同时计算线积分的2D数组，以便显着降低计算成本。在计算时间和准确性方面，我们将我们的算法与快速倾斜堆栈算法进行了比较。

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《Advances in Computational Methods in Sciences and Engineering 2005 vol.4A; Lecture Series on Computer and Computational Sciences; vol.4A》|2005年|P.319-322|共4页
会议地点 Loutraki(GR)
作者
O. Levi; B.A. Efros;
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作者单位

Department of Industrial Engineering and Management, Faculty of Engineering Sciences, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel;

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原文格式 PDF
正文语种 eng
中图分类计算数学的应用;
关键词
X-ray transform; radon transform; line integrals; fast slant-stack;

机译：X射线变换; rad变换;线积分;快速倾斜叠加;

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4. A New Fast Algorithm for Exact Calculation of the Discrete 2-D and 3-D X-Ray Transform [C] . O. Levi, B.A. Efros Advances in Computational Methods in Sciences and Engineering 2005 vol.4A; Lecture Series on Computer and Computational Sciences; vol.4A . 2005

机译：精确计算离散2-D和3-D X射线变换的新快速算法
5. Fast and Scalable Architectures and Algorithms for the Computation of the Forward and Inverse Discrete Periodic Radon Transform with Applications to 2D Convolutions and Cross-Correlations. [D] . Carranza, Cesar. 2016

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6. Discrete Radon transform has an exact fast inverse and generalizes to operations other than sums along lines [O] . William H. Press 2006

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7. Multirate and DFT Based Fast Parallel Algorithm for 2-D Inverse Discrete Gabor Transform [O] . Juan Juan Gu, Liang Tao 2016

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8. Comparison of Arithmetic Requirements for the PFA (Prime Factor Algorithm), WFTA (Winograd Fourier Transform Algorithm), SWIFT, MFFT (Mixed Radix Fast Fourier Transform), FFT (Fast Fourier Transform) and DFT (Discrete Fourier Transform) Algorithms. [R] . Hicks, R. C. 1982

机译：pFa（素因子算法），WFTa（Winograd傅立叶变换算法），sWIFT，mFFT（混合基线快速傅里叶变换），FFT（快速傅立叶变换）和DFT（离散傅立叶变换）算法的算术要求的比较。

A New Fast Algorithm for Exact Calculation of the Discrete 2-D and 3-D X-Ray Transform

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