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The primary goal of this work has been to develop a processing method for gated cardiac emission computed tomography (ECT) that simultaneously reconstructs the pixel intensities of the gated images and estimates the motion of the cardiac wall. The simultaneous reconstruction and motion estimation is achieved using conjugate gradient optimization with an objective function that is dependent on the gated reconstructed images at two time frames and the estimated motion of the object between the two frames. The method was evaluated on simulated phantom data both with and without Poisson noise. With noise-free data, the accuracy of the motion estimate and the quality of the reconstructed images were found to be dependent on the hyperparameter selection. With noisy data, the simultaneous method produced reconstructed images with smaller squared error compared with images reconstructed without motion estimation. In a patient gated myocardial perfusion study, the estimated motion between two frames agreed with subjective assessment of wall motion.