Maximum likelihood image reconstruction in positron emission tomography (PET):\sConvergence characteristics and stopping rules

Abstract

Maximum likelihood estimation image reconstruction algorithms for emission tomography received much attention during the last decade because of their potential to produce high quality images.\sA detailed study of the convergence properties of the expectation–maximization (EM) algorithm for PET image reconstruction is presented.\sThe main problems associated with this technique are addressed, namely, its high computational cost and the lack of a robust stopping criterion for this iterative algorithm.\sA practical implementation of the EM algorithm on a modern workstation is presented.\sA PET scanner is simulated using Monte Carlo techniques.\sDifferent kinds of data sets are produced and used in order to study the properties of the algorithm and develop a stopping rule, which are then validated with the use of real sinogram data from a commercial PET scanner.\sOther algorithms of the same iterative class are studied and modified versions of the EM algorithm are proposed with stopping rules, all based on the properties of the image vector updating coefficients in each iteration.\sA practical implementation of the EM algorithm is the final result, with optimal performance on the conventional computing systems available today, producing tomographic reconstructions in clinically meaningful times.