Fan-beam filtered-backprojection reconstruction without backprojection weight

In this paper, we address the problem of two-dimensional image reconstruction from fan-beam data acquired along a full 2π scan. Conventional approaches that follow the filtered-backprojection (FBP) structure require a weighted backprojection with the weight depending on the point to be reconstructed and also on the source position; this weight appears only in the case of divergent beam geometries. Compared to reconstruction from parallel-beam data, the backprojection weight implies an increase in computational effort and is also thought to have some negative impacts on noise properties of the reconstructed images. We demonstrate here that direct FBP reconstruction from full-scan fan-beam data is possible with no backprojection weight. Using computer-simulated, realistic fan-beam data, we compared our novel FBP formula with no backprojection weight to the use of an FBP formula based on equal weighting of all data. Comparisons in terms of signal-to-noise ratio, spatial resolution and computational efficiency are presented. These studies show that the formula we suggest yields images with a reduced noise level, at almost identical spatial resolution. This effect increases quickly with the distance from the center of the field of view, from 0% at the center to 20% less noise at 20 cm, and to 40% less noise at 25 cm. Furthermore, the suggested method is computationally less demanding and reduces computation time with a gain that was found to vary between 12% and 43% on the computers used for evaluation.