Assessment of Maximum A Posteriori Image Estimation Algorithms for Reduced Acquisition Time Medical Positron Emission Tomography Data

This study examines the effects of reduced radioactive dosage data collection on positron emission tomography reconstruction reliability and investigates the efficiency of various reconstruction methods. Also, it investigates properties of the reconstructed images under these circumstances and the limitations of the currently used algorithms. The methods are based on maximum likelihood and maximum a posteriori estimation, but no explicit solutions exist and hence iterative schemes are obtained using the expectation-maximisation and one-step-late methods, while greater efficiency is obtained by using an ordered-subset approach. Ten replicate real datasets, from the Hoffman brain phantom collected using a Siemens Biograph mMR scanner, are considered using standard deviation, bias and mean-squared error as quantitative output measures. The variability is very high when low prior parameter values are used but reduces substantially for higher values. However, in contrast, the bias is low for low parameter values and high for high parameter values. For individual reconstructions, low parameter values lead to detail being lost in the noise whereas high values produce unacceptable artefacts at the boundaries between different anatomical regions. Considering the mean-squared error, a balance between bias and variability, still identifies high prior parameter values as giving the best results, but this is in contradiction to visual inspection. These findings demonstrate that when it comes to low counts, variability and bias become significant and are visible in the images, but that improved reconstruction can be achieved by a careful choice of the prior parameter.