Accelerating 4D flow MRI by exploiting vector field divergence regularization

Claudio Santelli, Michael Loecher, Julia Busch, Oliver Wieben, Tobias Schaeffter, Sebastian Kozerke*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


Purpose: To improve velocity vector field reconstruction from undersampled four-dimensional (4D) flow MRI by penalizing divergence of the measured flow field. Theory and Methods: Iterative image reconstruction in which magnitude and phase are regularized separately in alternating iterations was implemented. The approach allows incorporating prior knowledge of the flow field being imaged. In the present work, velocity data were regularized to reduce divergence, using either divergence-free wavelets (DFW) or a finite difference (FD) method using the ℓ1-norm of divergence and curl. The reconstruction methods were tested on a numerical phantom and in vivo data. Results of the DFW and FD approaches were compared with data obtained with standard compressed sensing (CS) reconstruction. Results: Relative to standard CS, directional errors of vector fields and divergence were reduced by 55-60% and 38-48% for three- and six-fold undersampled data with the DFW and FD methods. Velocity vector displays of the numerical phantom and in vivo data were found to be improved upon DFW or FD reconstruction. Conclusion: Regularization of vector field divergence in image reconstruction from undersampled 4D flow data is a valuable approach to improve reconstruction accuracy of velocity vector fields.

Original languageEnglish
JournalMagnetic Resonance in Medicine
Publication statusAccepted/In press - 2015


  • 4D flow
  • Compressed sensing
  • Flow quantification
  • Phase regularization
  • Undersampling
  • Vector field divergence


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