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A model-based activity reconstruction in both the energy and spatial domains is developed that includes separate parameterization for any objects moving with known motion. This approach corrects for object motion, without smearing the stationary backdrop space. The goal is to simultaneously obtain an energy-dependent spatial map of the radiation field for the backdrop and for each parameterized moving object. Experimental results show that the method can successfully reconstruct the activity of moving objects while also revealing stationary sources in the backdrop. Also, by including the possibility of partial photon energy deposition in the detector in the model, the incident energy spectrum is reconstructed more accurately.