Accelerating 4D flow MRI by exploiting vector field divergence regularization
Claudio Santelli
Imaging Sciences and Biomedical Engineering, King's College London, United Kingdom
Institute for Biomedical Engineering, University and ETH Zurich, Switzerland
Drs. Santelli and Loecher contributed equally to this work.
Search for more papers by this authorMichael Loecher
Department of Medical Physics, University of Wisconsin-Madison, Madison, Wisconsin, USA
Drs. Santelli and Loecher contributed equally to this work.
Search for more papers by this authorJulia Busch
Institute for Biomedical Engineering, University and ETH Zurich, Switzerland
Search for more papers by this authorOliver Wieben
Department of Medical Physics, University of Wisconsin-Madison, Madison, Wisconsin, USA
Department of Radiology, University of Wisconsin-Madison, Madison, Wisconsin, USA
Search for more papers by this authorTobias Schaeffter
Imaging Sciences and Biomedical Engineering, King's College London, United Kingdom
Search for more papers by this authorCorresponding Author
Sebastian Kozerke
Imaging Sciences and Biomedical Engineering, King's College London, United Kingdom
Institute for Biomedical Engineering, University and ETH Zurich, Switzerland
Correspondence to: Sebastian Kozerke, Ph.D., Institute for Biomedical Engineering, University and ETH Zurich, Gloriastrasse 35, 8092 Zurich. E-mail:[email protected]Search for more papers by this authorClaudio Santelli
Imaging Sciences and Biomedical Engineering, King's College London, United Kingdom
Institute for Biomedical Engineering, University and ETH Zurich, Switzerland
Drs. Santelli and Loecher contributed equally to this work.
Search for more papers by this authorMichael Loecher
Department of Medical Physics, University of Wisconsin-Madison, Madison, Wisconsin, USA
Drs. Santelli and Loecher contributed equally to this work.
Search for more papers by this authorJulia Busch
Institute for Biomedical Engineering, University and ETH Zurich, Switzerland
Search for more papers by this authorOliver Wieben
Department of Medical Physics, University of Wisconsin-Madison, Madison, Wisconsin, USA
Department of Radiology, University of Wisconsin-Madison, Madison, Wisconsin, USA
Search for more papers by this authorTobias Schaeffter
Imaging Sciences and Biomedical Engineering, King's College London, United Kingdom
Search for more papers by this authorCorresponding Author
Sebastian Kozerke
Imaging Sciences and Biomedical Engineering, King's College London, United Kingdom
Institute for Biomedical Engineering, University and ETH Zurich, Switzerland
Correspondence to: Sebastian Kozerke, Ph.D., Institute for Biomedical Engineering, University and ETH Zurich, Gloriastrasse 35, 8092 Zurich. E-mail:[email protected]Search for more papers by this authorAbstract
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. Magn Reson Med 75:115–125, 2016. © 2015 Wiley Periodicals, Inc.
Supporting Information
Additional Supporting Information may be found in the online version of this article.
| Filename | Description |
|---|---|
| mrm25563-sup-0001-suppinfo1.docx1.7 MB | SUP. FIG. S1. Bland-Altman and linear correlation plots of peak flow measurements (R = 3). SUP. FIG. S2. Bland-Altman and linear correlation plots of peak flow measurements (R = 6). SUP. FIG. S3. Bland-Altman and linear correlation plots of total flow measurements (R = 3). SUP. FIG. S4. Bland-Altman and linear correlation plots of total flow measurements (R = 6). |
Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.
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