Investigation of Scattering Influence in Single-photon Emission Computed Tomography in Case of Proportional Scattering Medium

Measurement results in single photon emission computed tomography (SPECT) are affected by many different factors, radiation absorption, and scattering being the most important ones. The inverse exponential Radon transform was developed to take into account the effect of absorption, while methods similar to the exponential Radon transform considering the radiation scattering do not exist. This is due to the fact that the interaction of radiation with a high-scattering medium is described using the integrodifferential radiation transfer equation (RTE). This equation does not have an exact analytical solution. Various approximations are used to simplify the RTE. Of particular interest is the approximation of a proportional scattering medium (PSM). For PSM, a special type of scattering indicatrix is postulated, which makes it possible both to obtain the exact analytical solution to the RTE and to solve the inverse tomographic problem. There is presented the numerical simulation of SPECT in a PSM.