Numerical study of multigrid implementations of some iterative image reconstruction algorithms

The numerical behavior of multigrid implementations of the Landweber, generalized Landweber, ART (algebraic reconstruction technique), and MLEM (maximum-likelihood expectation-maximization) iterative image reconstruction algorithms is investigated. Comparisons between these algorithms, and with their single-grid implementations, are made on one small-scale synthetic PET (positron emission tomography) system, for phantom objects exhibiting different characteristics. The multigrid implementation was found to accelerate the convergence rate of high-frequency components of the image when the image possessed the local smoothness property. In other cases it was unhelpful, and may even slow down the convergence rate.<>