Joint Estimation of Activity Distribution and Attenuation Map for TOF-PET using Alternating Direction Method of Multiplier

Abstract

Recent advances in TOF PET joint estimation of activity and attenuation showed that activity and attenuation can be determined up to a global constant scale without severe crosstalk. MLAA was first proposed to estimate activity and attenuation map simultaneously, and then MLACF was developed to estimate activity and attenuation compensation factor (ACF). MLAA incorporated prior knowledge on the zero attenuation value outside body area to determine global scalar, but was slow to converge. MLACF converged much faster than MLAA, but required knowing total activity level in advance. We propose a new optimization method based on variable splitting and alternating direction method of multiplier (MLADMM). Our proposed MLADMM achieved fast convergence rate comparable to MLACF without knowing total activity level. MLADMM also has a potential to use more sophisticated MR-based prior for attenuation in PET-MR.