Backprojection with Fourier series expansion and FFT

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