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When performing dynamic studies using emission tomography the tracer distribution changes during acquisition of a single set of projections. This is particularly true for some positron emission tomography (PET) systems which, like single photon emission computed tomography (SPECT), acquire data over a limited angle at any time, with full projections obtained by rotation of the detectors. In this paper, an approach is proposed for processing data from these systems, applicable to either PET or SPECT. A method of interpolation, based on overlapped parabolas, is used to obtain an estimate of the total counts in each pixel of the projections for each required frame-interval, which is the total time to acquire a single complete set of projections necessary for reconstruction. The resultant projections are reconstructed using traditional filtered backprojection (FBP) and tracer kinetic parameters are estimated using a method which relies on counts integrated over the frame-interval rather than instantaneous values. Simulated data were used to illustrate the technique's capabilities with noise levels typical of those encountered in either PET or SPECT. Dynamic datasets were constructed, based on kinetic parameters for fluoro-deoxy-glucose (FDG) and use of either a full ring detector or rotating detector acquisition. For the rotating detector, use of the interpolation scheme provided reconstructed dynamic images with reduced artefacts compared to unprocessed data or use of linear interpolation. Estimates for the metabolic rate of glucose had similar bias to those obtained from a full ring detector.