Multiresolution expectation maximization reconstruction algorithm for positron emission tomography using wavelet processing

A number of algorithms based on estimation theory have been developed for image reconstruction in Positron Emission Tomography (PET). Maximum Likelihood estimation method based Expectation Maximization (EM) reconstruction algorithm has been shown to provide good quality reconstruction for PET. Conventional EM algorithm suffers from slow convergence and noisy reconstruction due to numerical errors which starts accumulating as the algorithm is iterated for longer duration. The multiresolution EM algorithm (MREM) is an attempt at improving the conventional EM through an effective use of multiresolution reconstruction grids and multiresolution detector space. The detectors comprising the PET detector ring are combined to result in a multiresolution detector space. This process leads to reorganization (rebinning) of the tube data thus generating data spaces at different detector levels. The algorithm begins iterating at the coarsest grid level using coarsest tube data. It switches both the grid and detector levels simultaneously until the finest detector and reconstruction grid resolution is 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