Robust solvers for inverse imaging problems using dense single-precision hardware
Journal of Mathematical Imaging and Vision
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In two dimensions, the exponential X-ray transform has been well-studied 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 three-dimensional (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-of-interest. The derivation is presented in the context of the RSH SPECT geometry. Results from computer simulations are given.