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 divergent (fan) X-ray beams. Fan-beam projection data require special reconstruction techniques to be implemented. Among reconstruction techniques from parallel projection data, the Direct Fourier Method (DFM) proved to be one of the most promising ones, especially for high-speed image reconstruction in the high-end 3-D and dynamic tomographic systems. The goal of the paper is to answer the topical question: how would direct use of the DFM influence the quality of image reconstruction from the fan-beam data? The formula describing the error caused by such an approximation is derived in the paper. The conclusions deduced from the formula are confirmed by computer simulations. Furthermore, the boundary values of data acquisition geometry parameters have been estimated for the case of using the DFM without recalculating the fan-beam data