Pressure reconstruction using velocity measurement-error based generalized least-squares

A pressure reconstruction method using the velocity measurement error to inform generalized least-squares (GLS) is introduced. An overdetermined linear system of equations is formulated to relate pressure with pressure gradients calculated from velocity field. Pressure field is obtained by solving the system using GLS with a weight matrix based on the accuracy of the pressure gradients. The weight matrix is generated based on pressure gradient errors by propagating the velocity errors calculated from spurious velocity divergence for incompressible flow. The pressure reconstruction method is demonstrated and analyzed using velocity fields from artificial images. The method is applied to flow in the geometry of a cerebral aneurysm. 3-dimensional velocity field is obtained using PTV with STB method. The pressure reconstruction method is validated by comparing the calculated pressure field with direct pressure measurements and CFD simulation. Application to in-vivo flow measurement by MRI is also included.