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A new dynamic image reconstruction method for PET is proposed. First, a set of exponential temporal basis functions is predefined, covering the entire range of kinetics (from static through to a delta function). Just as in spectral analysis, such a selection is designed to be able to handle all possible tissue responses for multi-compartmental tissue models. Second, an initial estimate of an input function is defined. The time-dependent PET radiotracer concentration is then modeled (through the system matrix in the reconstruction algorithm) as a superposition of the exponential temporal basis functions, convolved with the input function. The reconstruction method uses an expectation maximization (EM) algorithm to operate directly on the measured PET data in order to i. estimate the coefficients of the exponential functions, and ii. improve the estimate of the input function. The coefficients and the input function are estimated only as a means of regularizing the model of the time-dependent image: the final reconstruction is used with conventional post-reconstruction kinetic analysis, with a different input function if need be (as the estimated input function may not correspond to the true input function). Results from tests on simulated data reveal a simultaneous benefit of noise reduction and improved kinetic parameter estimates when compared to conventional methodology. The method is also demonstrated on measured HRRT PET data for an FDG study.