Cone Beam Reconstruction with Sources on a Curve

An inversion procedure is developed for reconstructing a function of compact support in $\mathbb{R}^3 $ from its divergent beam x-ray transform with sources on a curve. The results apply to many curves not satisfying the conditions of Tuy [SIAM J. Appl. Math., 43 (1983), pp. 546–552), for example, planar circles of sufficiently large radius. In some cases, estimates in Sobolev norms are established for the inversion operator.