Maximum Likelihood estimation based Expectation Maximization(EM) reconstruction algorithm  has been shown to provide good quality reconstruction for PET. Our previous work [2,3] introduced multigrid concept for PET image reconstruction using EM. The multiresolution EM (MREM) algorithm is an attempt to improve the EM based estimation through an effective use of multi-resolution grids in both image-reconstruction and detector spaces. The algorithm begins iterating at the coarsest grid level using tube data that has been re-organized (re-binned) at the coarsest detector level. It switches both the grid and detector levels simultaneously until the finest detector and grid resolution are reached. This algorithm incorporates a wavelet decomposition based transition criterion for switching grid levels and a wavelet spline based interpolation method for projecting the intermediate reconstruction from a specific grid level to the next finer grid.