Parametric Dictionary-Based Velocimetry for Echo PIV

We introduce a novel motion estimation approach for Echo PIV for the laminar and steady flow model. We mathematically formalize the motion estimation problem as a parametrization of a dictionary of particle trajectories by the physical flow parameter. We iteratively refine this unknown parameter by subsequent sparse approximations. We show smoothness of the adaptive flow dictionary that is a key for a provably convergent numerical scheme. We validate our approach on real data and show accurate velocity estimation when compared to the state-of-the-art cross-correlation method.