The reconstruction of dynamic particle configurations from finitely many measurements directly in the phase space of positions and velocities is often too high-dimensional to compute feasibly. This talk covers a dimension reduced problem, obtained by projecting phase space onto lower-dimensional subspaces via Radon transform. After presenting results for exact reconstruction and error estimates for noisy data, I will introduce an adaptation of the general problem specifically for magnetic resonance imaging (MRI), which is the topic of my Master?s Thesis.