Towards a Practical Implementation of the MLE Algorithm for Positron Emission Tomography

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Abstract
Recognizing that the quality of images obtained by application of the Maximum Likelihood Estimator (MLE) to Positron Emission Tomography (PET) and Single Photon Emission Tomography (SPECT) appears to be substantially better than those obtained by conventional methods, we have started to develop methods that will facilitate the necessary research for a good evaluation of the algorithm and may lead to its practical application for research and routine tomography. We have found that the non-linear MLE algorithm can be used with pixel sizes which are smaller than the sampling distance, without interpolation, obtaining excellent resolution and no noticeable increase in noise. We have studied the role of symmetry in reducing the amount of matrix element storage requirements for full size applications of the algorithm and have used that concept to carry out two reconstructions of the Derenzo phantom with data from the ECAT-III instrument. The results show excellent signal-to-noise (S/N) ratio, particularly for data with low total counts, excellent sharpness, but low contrast at high frequencies when using the Shepp-Vardi model for probability matrices.