Waldén J
Yale University, Department of Mathematics, New Haven, CT 06520, USA.
IEEE Trans Med Imaging. 2000 Mar;19(3):211-22. doi: 10.1109/42.845179.
We develop a direct Fourier method (DFM) for reconstructing a function from its X-ray projections. We introduce a framework that can be used to get a quantitative comparison between different choices of basis functions in the step of resampling from polar to Cartesian coordinates. We use the framework to compare polynomial interpolation, approximated sinc-functions, Gaussians, splines, and Kaiser-Bessel functions. The resulting algorithm is very fast, requiring 12.5N2 log2 N + 49N2 flops. Numerical experiments show it to be efficient.
我们开发了一种直接傅里叶方法（DFM），用于从其X射线投影重建函数。我们引入了一个框架，该框架可用于在从极坐标重采样到笛卡尔坐标的步骤中，对基函数的不同选择进行定量比较。我们使用该框架来比较多项式插值、近似 sinc 函数、高斯函数、样条函数和凯泽 - 贝塞尔函数。所得算法非常快，需要12.5N² log₂N + 49N² 次浮点运算。数值实验表明它是有效的。
