A transition criterion for the multigrid expectation maximization reconstruction algorithm for positron emission tomography

The multigrid expectation maximization algorithm (MGEM), an extension of the maximum likelihood (ML) algorithm, has been applied to the problem of reconstruction in positron emission tomography (PET). The MGEM algorithm implemented the expectation maximization (EM) algorithm at different image resolutions. The coarse grids were used to extract the low-frequency components and the finer grids to extract the high-frequency components. The convergence-rate of the MGEM algorithm was used to determine when to switch grid levels. A grid-level transition criterion which used the co-occurrence matrix statistics of the reconstructed image is presented. These statistics were computed on an image reconstructed from simulated PET data and provided a reliable transition criterion