Parametric images provide insight into the spatial distribution of physiological parameters, but they are often extremely noisy, due to low SNR of tomographic data. Direct estimation from projections allows accurate noise modeling, improving the results of post-reconstruction fitting. We propose a method, which we name kinetic compressive sensing (KCS), based on a hierarchical Bayesian model and on a novel reconstruction algorithm, that encodes sparsity of kinetic parameters. Parametric maps are reconstructed by maximizing the joint probability, with an Iterated Conditional Modes (ICM) approach, alternating the optimization of activity time series (OS-MAP-OSL), and kinetic parameters (MAP-LM). We evaluated the proposed algorithm on a simulated dynamic phantom: a bias/variance study confirmed how direct estimates can improve the quality of parametric maps over a post-reconstruction fitting, and showed how the novel sparsity prior can further reduce their variance, without affecting bias. Real FDG PET human brain data (Siemens mMR, 40min) images were also processed. Results enforced how the proposed KCS-regularized direct method can produce spatially coherent images and parametric maps, with lower spatial noise and better tissue contrast. A GPU-based open source implementation of the algorithm is provided.
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