Wavelet based multiresolution expectation maximization reconstruction algorithm for positron emission tomography (PET)

The Maximum Likelihood estimation based Expectation Maximization (EM) reconstruction algorithm has been shown to provide good quality reconstruction for PET. The authors´ previous work introduced the 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