Tomographic reconstruction of incompressible flow

In many experiments facilitating tomography the reconstruction problem is under-determined, meaning there are many possible solutions consistent with the measurements. If the sampling rate is fast relative to the typical evolution time, the known physical dynamics of the system can be used as additional reconstruction constraints. Here we demonstrate that incorporating the requirement of incompressible flow can improve significantly the fidelity of the reconstructed sequence. The incompressibility of the reconstruction is assured by requiring the conservation of the density moments. It is demonstrated that the "incompressible" reconstruction can be significantly more accurate than the reconstruction using standard methods. A consequence of the density moments' conservation is the conservation of the density histogram throughout the reconstructed sequence.