A multi grid maximum likelihood 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 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 non-uniform correction efficiency of each iteration making the algorithm very sensitive to the image-pattern. An efficient knowledge-based multi-grid reconstruction algorithm based on ML approach is presented to overcome these problems.