Single-photon emission computed tomography in the scattering medium with the property of “scattering straight back”

Abstract

The problem of radiation scattering in integral reconstruction algorithms for single-photon emission computed tomography (SPECT) has not been completely solved. This is primarily due to the fact that the radiation transport equation (RTE) does not have an exact analytical solution in general form for a scattering indicatrix corresponding to a real medium. A special form of the scattering indicatrix is proposed here that corresponds to a scattering medium with a property named “scattering straight back.” With this scattering indicatrix, it is possible to obtain an exact analytical solution of the RTE with exact boundary conditions for an arbitrary distribution of radiation sources. From this exact solution, a new expression can be obtained for the measured data, named as generalized attenuated exponential Radon transform. A new definition of projections is proposed to obtain an exact solution of the inverse tomographic problem. This solution has the same level of rigor as the exponential Radon transform for a purely absorbing medium. The proposed algorithm is compared with the traditional SPECT algorithm (the inverse exponential Radon transform) using Monte Carlo simulation based on the nuclear physics software package Geant4. It is demonstrated that the new method is superior to the traditional method in terms of both the standard deviation criterion and better visual distinction of the details in the reconstructed tomogram. The results obtained can be used to improve the existing algorithms for image reconstruction in SPECT, as well as to aid in developing new designs of emission tomographs.