上采样傅里叶级数展开和插值 FFT 的反向投影。

Backprojection by upsampled Fourier series expansion and interpolated FFT.

机构信息

Res. Lab. of Electron., MIT, Cambridge, MA.

出版信息

IEEE Trans Image Process. 1992;1(1):77-87. doi: 10.1109/83.128032.

Abstract

A fast backprojection method through the use of interpolated fast Fourier transform (FFT) is presented. The computerized tomography (CT) reconstruction by the convolution backprojection (CBP) method has produced precise images. However, the backprojection part of the conventional CBP method is not very efficient. The authors propose an alternative approach to interpolating and backprojecting the convolved projections onto the image frame. First, the upsampled Fourier series expansion of the convolved projection is calculated. Then, using a Gaussian function, it is projected by the aliasing-free interpolation of FFT bins onto a rectangular grid in the frequency domain. The total amount of computation in this procedure for a 512x512 image is 1/5 of the conventional backprojection method with linear interpolation. This technique also allows the arbitrary control of the frequency characteristics.

摘要

提出了一种通过使用插值快速傅里叶变换（FFT）的快速反投影方法。卷积反投影（CBP）方法的计算机断层扫描（CT）重建产生了精确的图像。然而，传统的 CBP 方法的反投影部分效率不是很高。作者提出了一种替代方法，用于对卷积后的投影进行插值和反投影到图像帧上。首先，计算卷积后的投影的上采样傅里叶级数展开。然后，使用高斯函数，通过无混叠的 FFT -bin 插值将其投影到频域中的矩形网格上。对于 512x512 图像，此过程的总计算量为传统线性插值反投影方法的 1/5。该技术还允许任意控制频率特性。