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.

An extension of Rife's discrete Fourier transform (DFT) interpolation into a complex form is presented. The method has several advantages over Rife's original formula. It can estimate the decay rate of the input sequence as well as the frequency, and does not require a square-root operation. An error analysis suggests a powerful but simple refinement step which can nearly attain the Cramer-Rao (CR) bound. An interpolation formula is derived, and its iteration into a refinement procedure is discussed. The procedure also allows the use of arbitrary windows to suppress the interference of other frequency components in the data that are typically found with real and/or damped sequences.>

A computerized tomography reconstruction technique with the fast Fourier transform (FFT) is discussed. A fast backprojection method through the use of interpolated FFT is presented. An approach to interpolating and backprojecting the convolved projections onto the image frame is proposed. First, the Fourier series expansion of the convolved projection is calculated. It is then projected onto a rectangular grid in the frequency domain, using the aliasing-free interpolation of FFT bins. The total amount of computation in this procedure for a 512*512 image is 1/6 of the conventional backprojection method with linear interpolation. This technique also allows arbitrary control of the frequency characteristics.>

An fast-Fourier-transform (FFT)-based procedure which synthesizes the waveform directly from the set of spectral components is presented. A Gaussian window function is introduced to deal with noninteger frequencies. There exists an optimal condition for the width of the window which minimizes the numerical error. Techniques for the generation of linear envelope, decay, and frequency modulation are presented. Numerical results verify the validity of this procedure.>