Use of scattered coincidences for emission-based estimation of attenuation map in PET

Attenuation correction in PET/MR is difficult due to the lack of X-ray or radionuclide transmission scans. Known approaches to estimating attenuation maps from PET emission data are based on true coincidences only and fail in highly symmetric situations. We present a method of extracting information about the attenuation distribution from scattered coincidences, even with perfect spherical symmetry of attenuation and activity. Using GATE simulations in a realistic scanner geometry combined with perfect energy resolution, we show how back-projections of scattered coincidences can provide an estimate of the attenuation map. This method may ultimately be used to complement existing approaches, such as for compensation of artifacts in segmentation-based attenuation correction, or for determination of a missing constant in Maximum Likelihood reconstruction of Activity and Attenuation.