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Temporal basis functions have been found to be effective for regularizing the time-varying image activities in dynamic emission tomography. By modelling the tracer distribution function at individual pixels as a linear combination of a set of basis functions, the reconstruction problem becomes that of estimating the weights of the basis functions. In this work, we explore the use of temporally adaptive regularization in the basis function domain, where spatial smoothing is enforced in an adaptive fashion according to the time-varying data statistics. In our experiments the proposed method was demonstrated using simulated Tc99m-Teboroxime SPECT imaging with the gated mathematical cardiac-torso (gMCAT) phantom. Our results show that the proposed approach can lead to more accurate reconstruction of the time activities, which is important for differentiation between a perfusion defect and the normal myocardium.