Numerical study of multigrid implementations of some iterative image reconstruction algorithms.

The numerical behavior of multigrid implementations of the Landweber, generalized Landweber, ART, and MLEM iterative image reconstruction algorithms is investigated. Comparisons between these algorithms, and with their single-grid implementations, are made on two small-scale synthetic PET systems, for phantom objects exhibiting different characteristics, and on one full-scale synthetic system, for a Shepp-Logan phantom. The authors also show analytically the effects of noise and initial condition on the generalized Landweber iteration, and note how to choose the shaping operator to filter out noise in the data, or to enhance features of interest in the reconstructed image. Original contributions include (1) numerical studies of the convergence rates of single-grid and multigrid implementations of the Landweber, generalized Landweber, ART, and MLEM iterations and (2) effects of noise and initial condition on the generalized Landweber iteration, with procedures for filtering out noise or enhancing image features.