Analysis of the direct Fourier method for computer tomography

The authors develop a direct Fourier method (DFM) for reconstructing a function from its X-ray projections. They 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. They use the framework to compare polynomial interpolation, approximated sinc-functions, Gaussians, splines, and Kaiser-Bessel functions. The resulting algorithm is very fast, requiring 12.5 N/sup 2/ log, N+49 N/sup 2/ flops. Numerical experiments show it to be efficient.