Abstract

We formulate and solve a generalized inverse Navier–Stokes boundary value problem for velocity field reconstruction and simultaneous boundary segmentation of noisy flow velocity images. We use a Bayesian framework that combines CFD , Gaussian processes, adjoint methods, and shape optimization in a unified and rigorous manner. With this framework, we find the velocity field and flow boundaries (i.e. the digital twin) that are most likely to have produced a given noisy image. We also calculate the posterior covariances of the unknown parameters and thereby deduce the uncertainty in the reconstructed flow. First, we verify this method on synthetic noisy images of 2-D flows. Then we apply it to experimental phase contrast magnetic resonance (PC-MRI) images of an axisymmetric flow at low (≃6) and high (>30) SNRs. We show that this method successfully reconstructs and segments the low SNR images, producing noiseless velocity fields that match the high SNR images, despite using 27 times less data. This framework also provides additional flow information, such as the pressure field and wall shear stress, accurately and with known error bounds. We demonstrate this on a synthetic 2-D representation of the flow through an aortic aneurysm to show its relevance to medical imaging.