To generate parametric images for dynamic PET, direct reconstruction from projection data is statistically more efficient than conventional indirect methods that perform image reconstruction and kinetic modeling in two separate steps. Existing direct reconstruction methods often use nonlinear compartmental models, which require the knowledge of model order. This paper presents a direct reconstruction approach using a linear spectral representation and does not require model order assumption. A Laplacian prior is used to ensure sparsity in the spectral representation. The resultant maximum a posteriori (MAP) formulation is solved by an expectation maximization shrinkage algorithm. A bias correction step is developed to improve the MAP estimate. Computer simulations show that the proposed method achieves better bias-variance tradeoff than a conventional indirect method for estimating parametric images from dynamic PET data.
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