Ray Transforms on a Conformal Class of Curves

Details Ray Transforms on a Conformal Class of Curves Ray Transforms on a Conformal Class of Curves

2010-11-01

arxiv.org/abs/1011.0453v3

Mathematics

Complex Variables

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Scientific paper

We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields defining the initial transport and recasting the problem in terms of complex-analytic function theory. Explicit inversion formulae are then given in a unified form. The method is then used to give inversion formulae for the attenuated ray transform.

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