Detection Efficiency Modeling and Joint Activity and Attenuation Reconstruction in Non-TOF 3-D PET from Multiple-Energy Window Data

Emission-based attenuation correction (AC) methods offer the possibility of overcoming quantification errors induced by conventional MR-based approaches in PET and Magnetic Resonance (MR) (PET/MR) imaging. However, the joint problem of determining AC and the activity of interest is strongly ill-posed in non-time-of-flight (TOF) PET. This can be improved by exploiting the extra information arising from low energy window photons, but the feasibility of this approach has only been studied with relatively simplistic analytic simulations so far. This manuscript aims to address some of the remaining challenges needed to handle realistic measurements; in particular, the detection efficiency (normalization) estimation for each energy window is investigated. An energy-dependent detection efficiency model is proposed, accounting for the presence of unscattered events in the lower energy window due to detector scatter. Geometric calibration factors are estimated prior to the reconstruction for both scattered and unscattered events. Different reconstruction methods are also compared. Results show that geometric factors differ markedly between the energy windows and that our analytical model corresponds in good approximation to Monte Carlo simulation; the multiple energy window reconstruction appears sensitive to input/model mismatch. Our method applies to Monte Carlo generated data but can be extended to measured data. This study is restricted to single scatter events.