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The collective behavior of levitated particles in a weakly ionized plasma (dusty plasma) has raised significant scientific interest. This is due to the complex array of forces acting on the particles and their potential to act as in situ diagnostics of the plasma environment. Ideally, the three-dimensional (3D) motion of many particles should be tracked for long periods of time. Typically, stereoscopic imaging using multiple cameras combined with particle image velocimetry is used to obtain a velocity field of many particles, yet this method is limited by its sample volume and short time scales. Here, we demonstrate a different, high-speed tomographic imaging method capable of tracking individual particles. We use a scanning laser sheet coupled to a single high-speed camera. We are able to identify and track tens of individual particles over centimeter length scales for several minutes, corresponding to more than 10 000 frames.