Inversion formulas for the broken-ray Radon transform

TL;DR

This paper derives explicit inversion formulas for the broken-ray Radon transform, enabling simultaneous reconstruction of absorption and scattering coefficients, and demonstrates their effectiveness through numerical testing.

Contribution

The paper introduces generalized inversion formulas for the broken-ray Radon transform, extending the classical filtered backprojection approach.

Findings

Formulas enable simultaneous reconstruction of absorption and scattering.

Numerical tests confirm the effectiveness of the derived formulas.

Generalizes the classical Radon transform inversion method.

Abstract

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.