A Multigrid Expectation Maximization Reconstruction Algorithm for Positron Emission Tomography

The problem of reconstruction in positron emission tomography (PET) is basically estimating the number of photon pairs emitted from the source. Using the concept of the maximum likelihood (ML) algorithm, the problem of reconstruction is reduced to determining an estimate of the emitter density that maximizes the probability of observing the actual detector count data over all possible emitter density distributions. A solution using this type of expectation maximization (EM) algorithm with a fixed grid size is severely handicapped by the slow convergence rate, the large computation time, and the nonuniform correction efficiency of each iteration making the algorithm very sensitive to the image pattern. An efficient knowledge-based multigrid reconstruction algorithm based on the ML approach is presented to overcome these problems.