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It is often necessary to estimate the parameters of a compartmental model from PET image data. These kinetic parameters are important because they quantify physiological processes. Existing methods for computing kinetic parametric images work by first reconstructing a sequence of PET images, and then estimating the kinetic parameters for each voxel location in the images. We propose a novel iterative tomographic reconstruction algorithm for directly computing a MAP estimate of the kinetic parameter image directly from dynamic PET sinogram data. This MAP reconstruction process estimates a vector of kinetic parameters at each voxel using explicit models of measurement noise, temporal tracer concentration, and spatial parameter variation. Experimental simulations using a two tissue compartment model show that our method can substantially reduce parameter estimation error.