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February  2014, 8(1): 103-125. doi: 10.3934/ipi.2014.8.103

Ray transforms on a conformal class of curves

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

Received  May 2010 Revised  October 2011 Published  March 2014

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.
Citation: Nicholas Hoell, Guillaume Bal. Ray transforms on a conformal class of curves. Inverse Problems & Imaging, 2014, 8 (1) : 103-125. doi: 10.3934/ipi.2014.8.103
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References:
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