A globally convergent regularized ordered-subset EM algorithm for list-mode reconstruction

Abstract

List-mode (LM) acquisition allows collection of data attributes at higher levels of precision than is possible with binned (i.e., histogram-mode) data. Hence, it is particularly attractive for low-count data in emission tomography. An LM likelihood and convergent EM algorithm for LM reconstruction was presented in Parra and Barrett, TMI, v17, 1998. Faster ordered subset (OS) reconstruction algorithms for LM 3-D PET were presented in Reader et al., Phys. Med. Bio., v43, 1998. However, these OS algorithms are not globally convergent and they also do not include regularization using convex priors which can be beneficial in emission tomographic reconstruction. LM-OSEM algorithms incorporating regularization via inter-iteration filtering were presented in Levkovitz et al., TMI, v20, 2001, but these are again not globally convergent. Convergent preconditioned conjugate gradient algorithms for spatio-temporal LM reconstruction incorporating regularization were presented in Nichols, et al., TMI, v21, 2002, but these do not use OS for speedup. In this work, we present a globally convergent and regularized ordered-subset algorithm for LM reconstruction. Our algorithm is derived using an incremental EM approach. We investigated the speedup of our LM OS algorithm (versus a non-OS version) for a SPECT simulation, and found that the speedup was somewhat less than that enjoyed by other OS-type algorithms.