Evaluation of task-oriented performance of several fully 3D PET reconstruction algorithms

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Abstract
The relative performance of 5 fully 3D PET reconstruction algorithms is evaluated. The algorithms are a filtered backprojection (FBP) method and 2 variants each of the EM-ML and ART iterative methods. For each of the iterative methods, 1 variant makes use of voxels and the other makes use of 'blobs' (spherically symmetric functions smoothly decaying to zero at their boundaries) as basis functions in its discrete reconstruction model. The methods are evaluated from the point of view of the efficacy of the reconstructions produced by them for 3 typical medical tasks - estimation of the average activity inside specific regions of interest, hot spots detection, and cold spots detection. A free parameter is allowed in the description of each of the 5 algorithms; the parameters are determined by a training process during which a value of the free parameter is selected which (nearly) maximizes a technical figure of merit. Such training and the actual comparative evaluation is done by making use of randomly generated phantoms and their projection data. The methodology allows assignation of levels of statistical significance to claims of the relative superiority of 1 algorithm over another for a particular task. It is found that using blobs as basis functions in the iterative algorithms is definitely advantageous over using voxels. This result has high statistical significance. (A visual illustration of it is given.) Comparing FBP, EM-ML using blobs, and ART using blobs, the authors do not find a clear difference in the overall performance of the investigated variants of the methods. If anything, their results suggest that ART using blobs may be the most efficacious of the 3.