Backprojection by upsampled Fourier series expansion and interpolated FFT

Author

Tabei, Makoto ; Ueda, Mitsuhiro

Author_Institution

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

Volume

1

Issue

1

fYear

1992

fDate

1/1/1992 12:00:00 AM

Firstpage

77

Lastpage

87

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 512×512 image is 1/5 of the conventional backprojection method with linear interpolation. This technique also allows the arbitrary control of the frequency characteristics

Keywords

computerised tomography; fast Fourier transforms; interpolation; picture processing; series (mathematics); CT; Gaussian function; aliasing-free interpolation; backprojection method; computerized tomography; convolution backprojection; convolved projection; frequency characteristics; frequency domain; image frame; interpolated FFT; interpolated fast Fourier transform; upsampled Fourier series expansion; Computed tomography; Convolution; Discrete Fourier transforms; Fast Fourier transforms; Filtering; Fourier series; Frequency response; Image reconstruction; Interpolation; Low pass filters;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/83.128032

Filename

128032