The Inversion of Ray Transforms on a Conformal Class of Curves

2010/11/15 by Hoell, Nicholas, Bal, Guillaume
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1011.3547

Abstract

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.

Related

• Ray Transforms on a Conformal Class of Curves
• Ray Transforms and Vector Fields
• Inversions of the windowed ray transform
• Inversion of the attenuated geodesic X-ray transform over functions and vector fields on simple surfaces
• Partial inversion of the 2D attenuated X-ray transform with data on an arc