ON THE POSSIBILITY OF DIRECT FOURIER RECONSTRUCTION FROM DIVERGENT-BEAM PROJECTIONS

A great number of tomographic systems, especially those equipped with fast data acquisition techniques, scan the objects investigated by div ergent (fan) X-ray beams. Fan-beam projection data require special rec onstruction techniques to be implemented. Among reconstruction techniq ues from parallel projection data, the Direct Fourier Method (DFM) pro ved to be one of the most promising ones, especially for high-speed im age reconstruction in the high-end 3-D and dynamic tomographic systems . The goal of our paper is to answer the topical question: how would d irect use of the DFM influence the quality of image reconstruction fro m the fan-beam data? The formula describing the error caused by such a n approximation is derived in the paper. The conclusions deduced from the formula are confirmed by computer simulations. Furthermore, the bo undary values of data acquisition geometry parameters have been estima ted for the case of using the DFM without recalculating the fan-beam d ata.