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Fast optimal pre-reconstruction filters for dynamic PET

Dynamic PET images are usually reconstructed one-by-one by methods designed for static images. This approach is suboptimal because it makes no use of information in the temporal correlations of the signal. Optimally, one should instead consider the entire dynamic study as a single space-time signal to be reconstructed. Unfortunately, direct implementation of this approach leads to a very time-consuming computation. However, the authors show that, by appropriate transformation of the imaging equation, one can achieve this goal with less computations than ordinary filtered backprojection (FBP) in some cases. The required steps are as follows: transform the sinograms to a reduced Karhunen-Loeve (KL) domain, restore them using a Wiener-type filter, apply FBP to reconstruct only the significant KL-coefficient images, then invert the KL transform to obtain a high-quality dynamic image sequence. Actual PET data and computer simulations are used to evaluate the method.