title: Accelerating 4D flow MRI by exploiting vector field divergence regularization.
abstract: OBJECTIVE
  To improve velocity vector field reconstruction from undersampled four-dimensional (4D) flow MRI by penalizing divergence of the measured flow field.
  
  
  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.
  
  
  CONCLUSIONS
  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.
authors: Imaging Sciences and Biomedical Engineering, King's College London, United Kingdom.|Institute for Biomedical Engineering, University and ETH Zurich, Switzerland.
authors: Claudio
authors: C
authors: Santelli
authors: Department of Medical Physics, University of Wisconsin-Madison, Madison, Wisconsin, USA.
authors: Michael
authors: M
authors: Loecher
authors: Institute for Biomedical Engineering, University and ETH Zurich, Switzerland.
authors: Julia
authors: J
authors: Busch
authors: Department of Medical Physics, University of Wisconsin-Madison, Madison, Wisconsin, USA.|Department of Radiology, University of Wisconsin-Madison, Madison, Wisconsin, USA.
authors: Oliver
authors: O
authors: Wieben
authors: Imaging Sciences and Biomedical Engineering, King's College London, United Kingdom.
authors: Tobias
authors: T
authors: Schaeffter
authors: Imaging Sciences and Biomedical Engineering, King's College London, United Kingdom.|Institute for Biomedical Engineering, University and ETH Zurich, Switzerland.
authors: Sebastian
authors: S
authors: Kozerke
mesh_terms: D000465:Algorithms; D001011:Aorta / Q000033:anatomy & histology* / Q000502:physiology*; D001783:Blood Flow Velocity / Q000502:physiology*; D005260:Female; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D018810:Magnetic Resonance Angiography / Q000379:methods*; D008297:Male; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
keywords: 4D flow; compressed sensing; flow quantification; phase regularization; undersampling; vector field divergence