We extend Grangeat's formula (1991) so that partially measured cone-beam projections can be incorporated into image reconstruction in a successful way. The extension is based on a simple fact that multiple partially measured projections may be combined to compute the 3-D Radon data inaccessible from any single orbit point. Furthermore, we show a few examples for which Grangeat's formula does not provide a method for exact reconstruction but the extended formula does.
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Kudo et al. (2002) studied this question.
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