3-D image reconstruction from exponential X-ray projections using Neumann series
نویسندگان
چکیده
In two dimensions, the exponential X-ray transform has been wellstudied due to its applications of correcting attenuation effects in Single Photon Emission Computed Tomography (SPECT). Explicit inversion formulas have been known for over 15 years. The threedimensional (3D) case has not been as thoroughly examined, and inversion formulas are available for only a few of the wide range of possible 3D geometries. The Rotating Slant-Hole (RSH) SPECT geometry is a special case for which no inversion formula has yet appeared. This paper presents a general inversion formula for the 3D exponential X-ray transform using a Neumann series. The method applies to any geometry but convergence of the series depends on the exponential scalar and the size of the region-ofinterest. The derivation is presented in the context of the RSH SPECT geometry. Results from computer simulations are given.
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