Inversion formulas for the broken-ray Radon transform

Details Inversion formulas for the broken-ray Radon transform Inversion formulas for the broken-ray Radon transform

2010-07-23

arxiv.org/abs/1007.4183v1

Inverse Problems 27, 025002 (2011)

Physics

Mathematical Physics

To be submitted to Inverse Problems

Scientific paper

10.1088/0266-5611/27/2/025002

We consider the inverse problem of the broken ray transform (sometimes also referred to as the V-line transform). Explicit image reconstruction formulas are derived and tested numerically. The obtained formulas are generalizations of the filtered backprojection formula of the conventional Radon transform. The advantages of the broken ray transform include the possibility to reconstruct the absorption and the scattering coefficients of the medium simultaneously and the possibility to utilize scattered radiation which, in the case of the conventional X-ray tomography, is typically discarded.

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