Maximum Likelihood Reconstruction for SPECT with Monte Carlo Modeling: Asymptotic Behavior

Inverse Monte Carlo (IMOC) reconstruction for SPECT uses a Maximum Likelihood (EM) estimator with detection probabilities generated as Monte Carlo solutions to the photon transport equation (PTE). To evaluate the behavior of the iterative EM algorithm, reconstructions from experimental projection data for up to 1000 iterations were examined. Compensation for scatter and attenuation was achieved by including those effects in the PTE. For uniform activity distributions, noise increased monotonically with iteration. With line sources included, both noise and resolution improved between 1 and 30 iterations after which resolution was slightly improved at the expense of noise. Contrast (for a nonactive region surrounded by activity) improved from 0.32 at 5 iterations to 0.90 at 200 iterations, and 0.97 at 1000. Uncertainty in the measurement increased due to increased noise in the active region.