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Direct application of the expectation maximisation (EM) algorithm to the spatiotemporal maximum likelihood problem results in a convenient separation of the image based problem from the projection based problem. This enables any spatiotemporal 4D image model to be incorporated into MLEM image reconstruction with relative ease, only requiring tailored calculation of the fitting weights. As a preliminary example, assessment using direct estimation of spectral analysis coefficients is presented, exploiting an image based non-negative least squares algorithm, where a specially-weighted least squares update is equivalent to the required update towards the maximum likelihood estimate. The proposed approach demonstrates a reduced root mean square error (RMSE) in the estimates of volume of distribution. Future work will include the exploration of alternative spatiotemporal models.