Joint reconstruction and segmentation of noisy velocity images as an inverse Navier–Stokes problem

We formulate and solve a generalized inverse Navier-Stokes problem for the joint velocity field reconstruction boundary segmentation of noisy flow images. To regularize we use Bayesian framework with Gaussian random fields. This allows us to estimate uncertainties unknowns by approximating their posterior covariance quasi-Newton method. first test method synthetic images 2D flows observe that successfully reconstructs segments signal-to-noise ratio (SNR) 3. Then conduct magnetic resonance velocimetry (MRV) experiment acquire an axisymmetric low ($\simeq 6$) high ($>30$) SNRs. show is capable reconstructing segmenting SNR images, producing noiseless fields smooth segmentation, negligible errors compared amounts reduction total scanning time factor 27. At same time, provides additional knowledge about physics (e.g. pressure), addresses shortcomings MRV (low spatial resolution partial volume effects) otherwise hinder accurate estimation wall shear stresses. Although implementation restricted steady planar flows, formulation applies immediately 3D naturally extends periodic unsteady flows.