The Attenuated Radon Transform Inversion Formula for Divergent Beam Geometry

A.A. Bukhgeim and S.G. Kazantsev (Russia)


Emission tomography, SPECT, fan-beam attenuated Radon transform, transport equation, inverse problems.


We consider the problem of two–dimensional single pho ton emission tomography (SPECT) in a case of a fan-beam geometry, which consists of recovering unknown emission map from SPECT data affected by a non-constant known attenuation coefficient. The straight line model (integral equation) is replaced by an inverse problem for a transport equation. In the case of the unit disk an explicit formula for recovering the emission map is derived. The numerical evaluation for the formula is presented.

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