Fast MLE for SPECT using an intermediate polar representation and a stopping criterion

The maximum-likelihood estimation (MLE) approach to SPECT (single-photon-emission computed tomography) has received considerable interest since the application of the expectation maximum (EM) algorithm to emission tomography. In addition to the appealing asymptotic properties of MLE solutions, the EM algorithm guarantees convergence to a positive solution. In practice, several drawbacks to an MLE approach are encountered: the computational demands are quite large, especially in comparison to noniterative techniques; reconstructions tend to take on an increasingly, nonsmooth quality as the MLE solution is approached, so the algorithm is usually terminated long before convergence. The authors address these problems in two ways: they perform the actual source estimation on a rectangular grid but use a polar pixel representation of the source during forward/back projection operations to reduce the computational requirements; they use a chi-squared test to statistically determine a suitable cutoff point for the iterative process.