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We investigated the imaging performance of a fast convergent ordered-subsets algorithm with subiteration-dependent preconditioners (SDPs) for positron emission tomography (PET) image reconstruction. In particular, we considered the use of SDP with the block sequential regularized expectation maximization (BSREM) approach with the relative difference prior (RDP) regularizer due to its prior clinical adaptation by vendors. Because the RDP regularization promotes smoothness in the reconstructed image, the directions of the gradients in smooth areas more accurately point toward the objective function's minimizer than those in variable areas. Motivated by this observation, two SDPs have been designed to increase iteration step-sizes in the smooth areas and reduce iteration step-sizes in the variable areas relative to a conventional expectation maximization preconditioner. The momentum technique used for convergence acceleration can be viewed as a special case of SDP. We have proved the global convergence of SDP-BSREM algorithms by assuming certain characteristics of the preconditioner. By means of numerical experiments using both simulated and clinical PET data, we have shown that the SDP-BSREM algorithms substantially improve the convergence rate, as compared to conventional BSREM and a vendor's implementation as Q.Clear. Specifically, SDP-BSREM algorithms converge 35\%-50\% faster in reaching the same objective function value than conventional BSREM and commercial Q.Clear algorithms. Moreover, we showed in phantoms with hot, cold and background regions that the SDP-BSREM algorithms approached the values of a highly converged reference image faster than conventional BSREM and commercial Q.Clear algorithms., Comment: 12 pages, 9 figures

Our aim was to enhance visual quality and quantitative accuracy of dynamic positron emission tomography (PET)uptake images by improved image reconstruction, using sophisticated sparse penalty models that incorporate both 2D spatial+1D temporal (3DT) information. We developed two new 3DT PET reconstruction algorithms, incorporating different temporal and spatial penalties based on discrete cosine transform (DCT)w/ patches, and tensor nuclear 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 and reconstructed. For the cardiac/lung phantom, an additional cardiac gated 2D-OSEM set was reconstructed. The structural similarity index (SSIM) and relative root mean squared error (rRMSE) relative ground truth was investigated. The image derived left ventricular (LV) volume for the cardiac/lung images was found by region growing and parametric images of the brain phantom were calculated. For the cardiac/lung phantom, 3DT-TNN yielded optimal images, and 3DT-DCT was best for the brain phantom. The optimal LV volume from the 3DT-TNN images was on average 11 and 55 percentage points closer to the true value compared to cardiac gated 2D-OSEM and 2D-OSEM respectively. Compared to 2D-OSEM, parametric images based on 3DT-DCT images generally had smaller bias and higher SSIM. Our novel methods that incorporate both 2D spatial and 1D temporal penalties produced dynamic PET images of higher quality than conventional 2D methods, w/o need for post-filtering. Breathing and cardiac motion were simultaneously captured w/o need for respiratory or cardiac gating. LV volumes were better recovered, and subsequently fitted parametric images were generally less biased and of higher quality., Comment: 11 pages, 12 figures