A direct Fourier method (DFM) for X-ray tomographic reconstructions and the accurate simulation of sinograms

This article illustrates the reconstruction of tomographic images by a direct Fourier method (DFM) and the results obtained from simulations and from experimental X-ray sinograms. The implementation of DFM, especially with regard to the resampling of the 2D Fourier transform, is based on a technique of Shannon reconstruction, devised by the authors, and on novel interpolating kernels. A short account is given on the principles and the implementation aspects of the interpolation technique. The DFM protocol developed by the authors has been tested, both for parallel and fan geometry, on simulated sinograms obtained from real images and from phantoms. The technique used to compute accurate projections is also described, since it might be useful in restoring missing parts of sinograms with processes based on ‘projections on convex sets’ (POCS) techniques. The results obtained from simulations and from the raw data of a third generation tomograph are presented and discussed. A comparison among reconstructions obtained from complete sinograms and from half of them suggests that adequate images could be obtained with a radiation dose lower than that used to obtain the experimental sinograms.