title: Analysis of the direct Fourier method for computer tomography.
abstract: We develop a direct Fourier method (DFM) for reconstructing a function from its X-ray projections. We 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. We use the framework to compare polynomial interpolation, approximated sinc-functions, Gaussians, splines, and Kaiser-Bessel functions. The resulting algorithm is very fast, requiring 12.5N2 log2 N + 49N2 flops. Numerical experiments show it to be efficient.
authors.affiliation: Yale University, Department of Mathematics, New Haven, CT 06520, USA. jwalden@math.yale.edu
authors.forename: J
authors.initials: J
authors.lastname: Waldén
mesh_terms: D000465:Algorithms; D005583:Fourier Analysis; D006801:Humans; D019047:Phantoms, Imaging; D015203:Reproducibility of Results; D014057:Tomography, X-Ray Computed / Q000592:standards