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In this paper we investigate the problem of simultaneously estimating the non-rigid motion vector field and the emission images in dynamic medical imaging procedures, such as gated cardiac ECT. We consider the case of two datasets, which, for instance, may be applied to the problem of determining the motion and emission intensities of the myocardium between end-diastole and end-systole gated cardiac data. Our method is based on minimizing an objective function consisting of a maximum likelihood image reconstruction term; the strain energy of an elastic material; and an image matching term that ensures a measure of agreement between the reference and deformed gated images. Minimization is achieved by a two-step iterative algorithm which alternately updates the motion vector field and the gated images. Simulations using exact and noisy datasets for a simple 2D phantom demonstrate the feasibility of the proposed method.