Three-dimensional image reconstruction from exponential parallel-beam projections

In this paper, we present a filtered-backprojection (FBP) algorithm suitable for image reconstruction from exponential X-ray (parallel-beam) projections sampled on any subset of the sphere that includes great circles. This algorithm is similar to the true three-dimensional reconstruction algorithm of Ra et al (1982) for nonattenuated projections. It is derived by combining all reconstructions that can be obtained from subsets of measurements corresponding to great circles. Our results generalize those published by Hazou (1988) and Weng et al. (1996) for reconstruction from projections sampled on the unit sphere. However, they remain modest, as they only apply to specific sets of measurements.