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We introduce a technique for recovering a sufficiently smooth function fromits ray transform over a wide class of curves in a general region of Euclideanspace. The method is based on a complexification of the underlying vectorfields defining the initial transport and recasting the problem in terms ofcomplex-analytic function theory. Explicit inversion formulae are then given ina unified form. The method is then used to give inversion formulae for theattenuated ray transform.

The Inversion of Ray Transforms on a Conformal Class of Curves