  Recovering pressure fields from image velocimetry measurements has two
general strategies: i) directly integrating the pressure gradients from the
momentum equation and ii) solving or enforcing the pressure Poisson equation
(divergence of the pressure gradients). In this work, we analyze the error
propagation of the former strategy and provide some practical insights. For
example, we establish the error scaling laws for the Pressure Gradient
Integration (PGI) and the Pressure Poisson Equation (PPE). We explain why
applying the Helmholtz-Hodge Decomposition (HHD) could significantly reduce the
error propagation for the PGI. We also propose to use a novel HHD-based
pressure field reconstruction strategy that offers the following advantages: i)
effective processing of noisy scattered or structured image velocimetry data on
a complex domain and ii) using Radial Basis Functions (RBFs) with
curl/divergence-free kernels to provide divergence-free correction to the
velocity fields for incompressible flows and curl-free correction for pressure
gradients. Complete elimination of divergence-free bias in measured pressure
gradient and curl-free bias in the measured velocity field results in superior
accuracy. Synthetic velocimetry data based on exact solutions and high-fidelity
simulations are used to validate the analysis as well as demonstrate the
flexibility and effectiveness of the RBF-HHD solver.
