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

Expectation maximization (EM) algorithm [1] and its derivatives have been applied to the problem of image reconstruction in Positron Emission Tomography (PET). The Multigrid Expectation Maximization (MGEM) algorithm [2] used the EM algorithm on a set of reconstruction grids with different resolutions. This paper introduces a Multiresolution Expectation Maximization (MREM) algorithm that extends the multiresolution approach of reconstruction grids in the MGEM algorithm to both image reconstruction and detector space. The detectors comprising the ring are re-organized to form a multiresolution detector space. The algorithm begins iterating at the coarsest grid level using tube data that has been re-binned at the coarsest detector level. It switches both the grid and detector levels simultaneously until the finest detector resolution is reached. The algorithm iterates further for various multi-resolution grid levels using the tube data at the finest detector resolution. This method provides faster convergence and better reconstruction than the conventional single grid EM (SGEM) algorithm. The MREM algorithm uses a new transition criterion for switching the grid-levels, which is developed using the high frequency energy derived from the wavelet decomposition of the reconstructed image at each iteration. It also uses a wavelet spline interpolation method used to project the intermediate reconstruction from a specific grid level to the next finer grid. The results of the MREM algorithm and the modified MGEM algorithm incorporating the wavelet decomposition based transition criterion and wavelet interpolation method on simulated phantom data and actual PET camera data are presented.