Physics-Informed Compressed Sensing (PICS) for joint reconstruction and segmentation of sparse PC-MRI signals: a digital-twin approach

Compressed sensing (CS) methods perform well at magnitude reconstruction, but accurate velocity (phase difference) reconstruction remains a challenge. We address this by extending the standard notion of sparsity used in CS methods to a more general notion of a structure, which is dictated by the Navier–Stokes (N-S) problem (physics-informed compressed sensing, PICS). We formulate PICS in a Bayesian framework, and use an inverse N-S problem to jointly reconstruct and segment the most likely velocity field, and at the same time infer hidden quantities such as the hydrodynamic pressure and the wall shear stress. We create an algorithm that solves this inverse problem, and test it for noisy/sparse k-space signals of the flow through a converging nozzle. We find that the method is capable of reconstructing/segmenting the velocity fields from sparsely-sampled, low signal-to-noise ratio (SNR) signals, and that the reconstructed velocity field compares well with that derived from fully-sampled high SNR signals of the same flow. Unlike CS methods, which only provide the reconstructed magnitude and velocity images, PICS learns the most likely digital twin of the measured flow. It can therefore be used to model new flow conditions, enabling patient-specific cardiovascular modelling.