Ray transforms on a conformal class of curves

Nicholas Hoell; Guillaume Bal

doi:10.3934/ipi.2014.8.103

Article Contents

2014, Volume 8, Issue 1: 103-125. Doi: 10.3934/ipi.2014.8.103

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Ray transforms on a conformal class of curves

Nicholas Hoell^1, and
Guillaume Bal^2,

1.
University of Toronto, Department of Mathematics, Toronto, ON, M5S 2E4
2.
Columbia University, Department of Applied Physics and Applied Mathematics, New York, NY, 10025

Received: May 2010

Revised: October 2011

Published: February 2014

Abstract / Introduction Related Papers Cited by

Abstract

We introduce a technique for recovering a sufficiently smooth function from its ray transforms over rotationally related curves in the unit disc of 2-dimensional Euclidean space. The method is based on a complexification of the underlying vector fields defining the initial transport and inversion formulae are then given in a unified form. The method is used to analyze the attenuated ray transform in the same setting.

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Mathematics Subject Classification: Primary: 35R30, 35F45; Secondary: 53C65.

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