Ray transforms on a conformal class of curves
Nicholas Hoell Guillaume Bal
Inverse Problems & Imaging 2014, 8(1): 103-125 doi: 10.3934/ipi.2014.8.103
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.
keywords: Beltrami equation quasiconformal harmonic Transport equation filtered backprojection. attenuated ray transform

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