The manuscripts presents the working principle of a novel technique to interpolate sparse and scattered particle tracking velocimetry (PTV) measurements onto a dense grid, by using the velocity measurements along a full particle trajectory. The method performs iteratively a vortex-in-cell simulation (Schneiders et al. 2014 in Exp Fluids 55:1692) to minimize the difference between the simulation and the scattered velocity measurements. The optimization is solved using the L-BFGS algorithm where gradients are evaluated efficiently using the adjoint of the vortex-in-cell code. In the numerical assessment, the case of a vortex is considered. At a given seeding concentration, the reconstruction quality of velocity was shown to improve by 50% when a full track is used in comparison to a divergence free reconstruction using only instantaneous velocity. The numerical assessment demonstrates the potential of the method to increase measurement quality and spatial resolution, in comparison to techniques that interpolate velocity using only instantaneous flow information and for example the divergence free constraint.@en