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A challenge in gated cardiac single photon emission computed tomography (SPECT) is the presence of increased imaging noise owing to gated data acquisition. In this study we propose a joint reconstruction approach for gated SPECT in which the different gate frames are reconstructed in a collective fashion by taking advantage of the statistics of the acquired data. Besides spatial smoothing, we use Fourier basis functions to regulate the time activities at each spatial location across the different gates, which are periodic owning to the periodic cardiac motion. We demonstrate the proposed approach by simulating gated Tc-99m labeled sestamibi imaging based on the NURBS-based cardiac-torso (NCAT) phantom.