Log-likelihood-based rule for image quality monitoring in the MLEM-based image reconstruction for PET

We address here the problem of the noise deterioration of the quality of the reconstructed images when employing the maximum likelihood expectation maximization (MLEM) algorithm for iterative image reconstruction in positron emission tomography (PET). It is observed that despite the fact the cost function (log-likelihood) is monotonically increasing, the image quality deteriorates after reaching a certain ¿optimum¿ point during the iterative process. The principal aim of the work is the discovery of a rule that would directly link the quality of the reconstructed images at each iteration with the log-likelihood. We assume that the true image corresponds to a log-likelihood value in correlation with the data acquired, which, when achieved, makes no sense looking for higher log-likelihood levels. We study here the hypothesis that there is a direct correlation of the log-likelihood of the true image (a quantity that is not known a priori in real PET scans) and acquired data, with certain properties of the pixel updating coefficients (PUC) in the MLEM algorithm. For the validation of this hypothesis we have employed Monte Carlo experiments using known phantoms. We show here that the minimum value of the PUC for the non-zero pixels might be one parameter that could be used to verify the above mentioned hypothesis.