Title :
Analysis of the direct Fourier method for computer tomography
Author_Institution :
Dept. of Math., Yale Univ., New Haven, CT, USA
fDate :
3/1/2000 12:00:00 AM
Abstract :
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 2 log, N+49 N 2 flops. Numerical experiments show it to be efficient.
Keywords :
computerised tomography; image reconstruction; interpolation; medical image processing; polynomials; splines (mathematics); Cartesian coordinates; Gaussians; Kaiser-Bessel functions; X-ray projections; basis functions; direct Fourier method; function reconstruction; medical diagnostic imaging; numerical experiments; polynomial interpolation; resampling; sinc-functions; Design for manufacture; Fourier transforms; Gaussian approximation; Image quality; Image reconstruction; Interpolation; Polynomials; Tomography; Two dimensional displays; X-ray imaging; Algorithms; Fourier Analysis; Humans; Phantoms, Imaging; Reproducibility of Results; Tomography, X-Ray Computed;
Journal_Title :
Medical Imaging, IEEE Transactions on
