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Our aim was to enhance visual quality and quantitative accuracy of dynamicpositron emission tomography (PET)uptake images by improved imagereconstruction, using sophisticated sparse penalty models that incorporate both2D spatial+1D temporal (3DT) information. We developed two new 3DT PETreconstruction algorithms, incorporating different temporal and spatialpenalties based on discrete cosine transform (DCT)w/ patches, and tensornuclear norm (TNN) w/ patches, and compared to frame-by-frame methods;conventional 2D ordered subsets expectation maximization (OSEM) w/post-filtering and 2D-DCT and 2D-TNN. A 3DT brain phantom with kinetic uptake(2-tissue model), and a moving 3DT cardiac/lung phantom was simulated andreconstructed. For the cardiac/lung phantom, an additional cardiac gated2D-OSEM set was reconstructed. The structural similarity index (SSIM) andrelative root mean squared error (rRMSE) relative ground truth wasinvestigated. The image derived left ventricular (LV) volume for thecardiac/lung images was found by region growing and parametric images of thebrain phantom were calculated. For the cardiac/lung phantom, 3DT-TNN yieldedoptimal images, and 3DT-DCT was best for the brain phantom. The optimal LVvolume from the 3DT-TNN images was on average 11 and 55 percentage pointscloser to the true value compared to cardiac gated 2D-OSEM and 2D-OSEMrespectively. Compared to 2D-OSEM, parametric images based on 3DT-DCT imagesgenerally had smaller bias and higher SSIM. Our novel methods that incorporateboth 2D spatial and 1D temporal penalties produced dynamic PET images of higherquality than conventional 2D methods, w/o need for post-filtering. Breathingand cardiac motion were simultaneously captured w/o need for respiratory orcardiac gating. LV volumes were better recovered, and subsequently fittedparametric images were generally less biased and of higher quality.

Dynamic PET cardiac and parametric image reconstruction: a fixed-point  proximity gradient approach using patch-based DCT and tensor SVD  regularization