In this paper we give a characterization of the range of the divergent beam x-ray transform when the source set is a sphere. The result is analogous to the theorem of Helgason [Acta. Math., 113 (1965), pp. 153–180] and Ludwig [Comm. Pure Appl. Math., 69 (1966), pp. 49–81] on the range of the Radon transform.
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Finch et al. (1983) studied this question.
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