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In image reconstruction gated acquisition is often used in order to deal with blur caused by organ motion in the resulting images. However, this is achieved almost inevitably at the expense of reduced signal-to-noise ratio in the acquired data. In this work, we propose a reconstruction procedure for gated images based upon use of discrete Fourier transform (DFT) basis functions, wherein the temporal activity at each spatial location is regulated by a Fourier representation. The gated images are then reconstructed through determination of the coefficients of the Fourier representation. We demonstrate this approach in the context of single photon emission computed tomography (SPECT) for cardiac imaging, which is often hampered by the increased noise due to gating and other degrading factors. We explore two different reconstruction algorithms, one is a penalized least-square approach and the other is a maximum a posteriori approach. In our experiments, we conducted a quantitative evaluation of the proposed approach using Monte Carlo simulated SPECT imaging. The results demonstrate that use of DFT-basis functions in gated imaging can improve the accuracy of the reconstruction. As a preliminary demonstration, we also tested this approach on a set of clinical acquisition.