Physics-Informed Compressed Sensing for PC-MRI: An Inverse Navier-Stokes Problem

We formulate a physics-informed compressed sensing (PICS) method for the reconstruction of velocity fields from noisy and sparse phase-contrast magnetic resonance signals. The method solves an inverse Navier-Stokes boundary value problem, which permits us to jointly reconstruct and segment the veloc...

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Bibliographic Details
Published in:IEEE transactions on image processing 2023-01, Vol.32, p.281-294
Main Authors: Kontogiannis, Alexandros, Juniper, Matthew P.
Format: Article
Language:English
Subjects:
Algorithms
Boundary conditions
Boundary value problems
Compressed sensing
Fields (mathematics)
Fluid flow
Hydrodynamic pressure
Image reconstruction
Inverse problems
Magnetic resonance
Magnetic resonance imaging
Navier-Stokes equations
Noise measurement
Phase-contrast magnetic resonance imaging (PC-MRI)
physics-informed compressed sensing
Reconstruction
Signal to noise ratio
Stress
Velocity
Velocity distribution
Velocity measurement
velocity reconstruction and segmentation
Wall shear stresses
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Summary:We formulate a physics-informed compressed sensing (PICS) method for the reconstruction of velocity fields from noisy and sparse phase-contrast magnetic resonance signals. The method solves an inverse Navier-Stokes boundary value problem, which permits us to jointly reconstruct and segment the velocity field, and at the same time infer hidden quantities such as the hydrodynamic pressure and the wall shear stress. Using a Bayesian framework, we regularize the problem by introducing a priori information about the unknown parameters in the form of Gaussian random fields. This prior information is updated using the Navier-Stokes problem, an energy-based segmentation functional, and by requiring that the reconstruction is consistent with the k -space signals. We create an algorithm that solves this inverse problem, and test it for noisy and sparse k -space signals of the flow through a converging nozzle. We find that the method is capable of reconstructing and segmenting the velocity fields from sparsely-sampled (15% k -space coverage), low ( \sim 10 ) signal-to-noise ratio (SNR) signals, and that the reconstructed velocity field compares well with that derived from fully-sampled (100% k -space coverage) high ( > 40 ) SNR signals of the same flow.
ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2022.3228172