Feasibility of scatter based electron density reconstruction for attenuation correction in positron emission tomography

Attenuation correction is required for quantitative analysis in positron emission tomography (PET). At PET energies, the attenuation coefficient may be approximated by the product of the Klein-Nishina cross-section per electron and the electron density. We have evaluated the feasibility of reconstructing the electron density directly from measured PET scatter events in order to obtain the attenuation map without a transmission scan. A scatter model was developed which describes the possible scattering locations for single-scatter coincidences. The expected number of coincidences detected by each detector pair was formulated based on the model. For this study, we ignored the attenuation of the scattered coincidences and a maximum likelihood expectation maximization (MLEM) algorithm was derived. We tested the method using a 2-dimensinal ring phantom with different activity distributions and a NEMA image quality phantom. For both phantoms we obtained little cross-talk between the activity and attenuation map. The attenuation of the scattered photons needs to be included in order to achieve a more accurate reconstruction.