Accelerating 4D flow MRI by exploiting vector field divergence regularization

TY - JOUR

T1 - Accelerating 4D flow MRI by exploiting vector field divergence regularization

AU - Santelli, Claudio

AU - Loecher, Michael

AU - Busch, Julia

AU - Wieben, Oliver

AU - Schaeffter, Tobias

AU - Kozerke, Sebastian

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - 4D flow

KW - Compressed sensing

KW - Flow quantification

KW - Phase regularization

KW - Undersampling

KW - Vector field divergence

UR - http://www.scopus.com/inward/record.url?scp=84923072318&partnerID=8YFLogxK

U2 - 10.1002/mrm.25563

DO - 10.1002/mrm.25563

M3 - Article

AN - SCOPUS:84923072318

SN - 0740-3194

JO - Magnetic Resonance in Medicine

JF - Magnetic Resonance in Medicine

ER -