  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.
