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In standard SPECT with static radio-tracers, the activity distribution in tissue is assumed constant during the acquisition. However, techniques capable of visualizing dynamic tracers may provide new insight into physiology and function of organisms. This is the aim of dynamic SPECT. We developed oSPECT, a new fully 4D reconstruction approach to obtain time activity curves from single or multiple slow rotations with dynamic SPECT data. It is based on KNITRO, a large-scale nonlinear constrained optimization method that takes curvature information into account to speed up convergence. The performance of oSPECT is tested using data from a dynamic anthropomorphic numerical phantom that simulates myocardial perfusion of 99mTc-Teboroxime. We also tested the method on a simulated brain study with 123I-FP-CIT, a dynamic presynaptic marker for SPECT of the dopaminergic neurotransmission system.