4-D PET joint image reconstruction/non-rigid motion estimation with limited MRI prior information

Institute of Nuclear Medicine–UCL, University College London, London NW1 2BU, UK Motion compensated gated PET image reconstruction methods include jointreconstruction (JR) and indirect reconstruction (IR) with pre-estimated motion from MRI (MRI-IR). JR suffers from poor PET data quality whereas MRI-IR requires highquality MRI volumes at each gate. We propose a penalised maximum-likelihood approach combining JR and MRI-IR. Our method is referred to as minimal MRI prior JR (MP-JR). The M gates data are stored in g = [g1; ...; gM] where gm is the measurement vector at gate m. Each gm is a Poisson distributed vector of parameter g f P f r ( , ) ( )   m m m W   where P is the projector, W(am) is the m-th motion of parameter am, rm is the m-th average random/scatter vector and f is the activity at m = 1. JR is achieved with (1).