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Inversion of the 3D exponential parallel-beam transform and the Radon transform with angle-dependent attenuation

2004
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Inverse Problems
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The inversion problem for the 3D parallel-beam exponential ray transform is solved through inversion of a set of the 2D exponential Radon transforms with complex-valued angle-dependent attenuation. An inversion formula for the latter 2D transform is derived; it generalizes the known Kuchment-Shneiberg formula valid for real angle-dependent attenuation. We derive an explicit theoretically exact solution of the 3D problem which is valid for arbitrary closed trajectory that does not intersect

doi:10.1088/0266-5611/20/5/008
fatcat:eofihptv2jhjpaixrgtym5mcaq