Hybrid data fidelity term approach for quantitative susceptibility mapping
Purpose Susceptibility maps are usually derived from local magnetic field estimations by minimizing a functional composed of a data consistency term and a regularization term. The data‐consistency term measures the difference between the desired solution and the measured data using typically the L2‐...
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| Vydáno v: | Magnetic resonance in medicine Ročník 88; číslo 2; s. 962 - 972 |
|---|---|
| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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United States
Wiley Subscription Services, Inc
01.08.2022
John Wiley and Sons Inc |
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| ISSN: | 0740-3194, 1522-2594, 1522-2594 |
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| Abstract | Purpose
Susceptibility maps are usually derived from local magnetic field estimations by minimizing a functional composed of a data consistency term and a regularization term. The data‐consistency term measures the difference between the desired solution and the measured data using typically the L2‐norm. It has been proposed to replace this L2‐norm with the L1‐norm, due to its robustness to outliers and reduction of streaking artifacts arising from highly noisy or strongly perturbed regions. However, in regions with high SNR, the L1‐norm yields a suboptimal denoising performance. In this work, we present a hybrid data fidelity approach that uses the L1‐norm and subsequently the L2‐norm to exploit the strengths of both norms.
Methods
We developed a hybrid data fidelity term approach for QSM (HD‐QSM) based on linear susceptibility inversion methods, with total variation regularization. Each functional is solved with ADMM. The HD‐QSM approach is a two‐stage method that first finds a fast solution of the L1‐norm functional and then uses this solution to initialize the L2‐norm functional. In both norms we included spatially variable weights that improve the quality of the reconstructions.
Results
The HD‐QSM approach produced good quantitative reconstructions in terms of structural definition, noise reduction, and avoiding streaking artifacts comparable with nonlinear methods, but with higher computational efficiency. Reconstructions performed with this method achieved first place at the lowest RMS error category in stage 1 of the 2019 QSM Reconstruction Challenge.
Conclusions
The proposed method allows robust and accurate QSM reconstructions, obtaining superior performance to state‐of‐the‐art methods. |
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| AbstractList | Susceptibility maps are usually derived from local magnetic field estimations by minimizing a functional composed of a data consistency term and a regularization term. The data-consistency term measures the difference between the desired solution and the measured data using typically the L2-norm. It has been proposed to replace this L2-norm with the L1-norm, due to its robustness to outliers and reduction of streaking artifacts arising from highly noisy or strongly perturbed regions. However, in regions with high SNR, the L1-norm yields a suboptimal denoising performance. In this work, we present a hybrid data fidelity approach that uses the L1-norm and subsequently the L2-norm to exploit the strengths of both norms.
We developed a hybrid data fidelity term approach for QSM (HD-QSM) based on linear susceptibility inversion methods, with total variation regularization. Each functional is solved with ADMM. The HD-QSM approach is a two-stage method that first finds a fast solution of the L1-norm functional and then uses this solution to initialize the L2-norm functional. In both norms we included spatially variable weights that improve the quality of the reconstructions.
The HD-QSM approach produced good quantitative reconstructions in terms of structural definition, noise reduction, and avoiding streaking artifacts comparable with nonlinear methods, but with higher computational efficiency. Reconstructions performed with this method achieved first place at the lowest RMS error category in stage 1 of the 2019 QSM Reconstruction Challenge.
The proposed method allows robust and accurate QSM reconstructions, obtaining superior performance to state-of-the-art methods. PurposeSusceptibility maps are usually derived from local magnetic field estimations by minimizing a functional composed of a data consistency term and a regularization term. The data‐consistency term measures the difference between the desired solution and the measured data using typically the L2‐norm. It has been proposed to replace this L2‐norm with the L1‐norm, due to its robustness to outliers and reduction of streaking artifacts arising from highly noisy or strongly perturbed regions. However, in regions with high SNR, the L1‐norm yields a suboptimal denoising performance. In this work, we present a hybrid data fidelity approach that uses the L1‐norm and subsequently the L2‐norm to exploit the strengths of both norms.MethodsWe developed a hybrid data fidelity term approach for QSM (HD‐QSM) based on linear susceptibility inversion methods, with total variation regularization. Each functional is solved with ADMM. The HD‐QSM approach is a two‐stage method that first finds a fast solution of the L1‐norm functional and then uses this solution to initialize the L2‐norm functional. In both norms we included spatially variable weights that improve the quality of the reconstructions.ResultsThe HD‐QSM approach produced good quantitative reconstructions in terms of structural definition, noise reduction, and avoiding streaking artifacts comparable with nonlinear methods, but with higher computational efficiency. Reconstructions performed with this method achieved first place at the lowest RMS error category in stage 1 of the 2019 QSM Reconstruction Challenge.ConclusionsThe proposed method allows robust and accurate QSM reconstructions, obtaining superior performance to state‐of‐the‐art methods. Susceptibility maps are usually derived from local magnetic field estimations by minimizing a functional composed of a data consistency term and a regularization term. The data-consistency term measures the difference between the desired solution and the measured data using typically the L2-norm. It has been proposed to replace this L2-norm with the L1-norm, due to its robustness to outliers and reduction of streaking artifacts arising from highly noisy or strongly perturbed regions. However, in regions with high SNR, the L1-norm yields a suboptimal denoising performance. In this work, we present a hybrid data fidelity approach that uses the L1-norm and subsequently the L2-norm to exploit the strengths of both norms.PURPOSESusceptibility maps are usually derived from local magnetic field estimations by minimizing a functional composed of a data consistency term and a regularization term. The data-consistency term measures the difference between the desired solution and the measured data using typically the L2-norm. It has been proposed to replace this L2-norm with the L1-norm, due to its robustness to outliers and reduction of streaking artifacts arising from highly noisy or strongly perturbed regions. However, in regions with high SNR, the L1-norm yields a suboptimal denoising performance. In this work, we present a hybrid data fidelity approach that uses the L1-norm and subsequently the L2-norm to exploit the strengths of both norms.We developed a hybrid data fidelity term approach for QSM (HD-QSM) based on linear susceptibility inversion methods, with total variation regularization. Each functional is solved with ADMM. The HD-QSM approach is a two-stage method that first finds a fast solution of the L1-norm functional and then uses this solution to initialize the L2-norm functional. In both norms we included spatially variable weights that improve the quality of the reconstructions.METHODSWe developed a hybrid data fidelity term approach for QSM (HD-QSM) based on linear susceptibility inversion methods, with total variation regularization. Each functional is solved with ADMM. The HD-QSM approach is a two-stage method that first finds a fast solution of the L1-norm functional and then uses this solution to initialize the L2-norm functional. In both norms we included spatially variable weights that improve the quality of the reconstructions.The HD-QSM approach produced good quantitative reconstructions in terms of structural definition, noise reduction, and avoiding streaking artifacts comparable with nonlinear methods, but with higher computational efficiency. Reconstructions performed with this method achieved first place at the lowest RMS error category in stage 1 of the 2019 QSM Reconstruction Challenge.RESULTSThe HD-QSM approach produced good quantitative reconstructions in terms of structural definition, noise reduction, and avoiding streaking artifacts comparable with nonlinear methods, but with higher computational efficiency. Reconstructions performed with this method achieved first place at the lowest RMS error category in stage 1 of the 2019 QSM Reconstruction Challenge.The proposed method allows robust and accurate QSM reconstructions, obtaining superior performance to state-of-the-art methods.CONCLUSIONSThe proposed method allows robust and accurate QSM reconstructions, obtaining superior performance to state-of-the-art methods. Purpose Susceptibility maps are usually derived from local magnetic field estimations by minimizing a functional composed of a data consistency term and a regularization term. The data‐consistency term measures the difference between the desired solution and the measured data using typically the L2‐norm. It has been proposed to replace this L2‐norm with the L1‐norm, due to its robustness to outliers and reduction of streaking artifacts arising from highly noisy or strongly perturbed regions. However, in regions with high SNR, the L1‐norm yields a suboptimal denoising performance. In this work, we present a hybrid data fidelity approach that uses the L1‐norm and subsequently the L2‐norm to exploit the strengths of both norms. Methods We developed a hybrid data fidelity term approach for QSM (HD‐QSM) based on linear susceptibility inversion methods, with total variation regularization. Each functional is solved with ADMM. The HD‐QSM approach is a two‐stage method that first finds a fast solution of the L1‐norm functional and then uses this solution to initialize the L2‐norm functional. In both norms we included spatially variable weights that improve the quality of the reconstructions. Results The HD‐QSM approach produced good quantitative reconstructions in terms of structural definition, noise reduction, and avoiding streaking artifacts comparable with nonlinear methods, but with higher computational efficiency. Reconstructions performed with this method achieved first place at the lowest RMS error category in stage 1 of the 2019 QSM Reconstruction Challenge. Conclusions The proposed method allows robust and accurate QSM reconstructions, obtaining superior performance to state‐of‐the‐art methods. |
| Author | Milovic, Carlos Tejos, Cristian Langkammer, Christian Lambert, Mathias |
| AuthorAffiliation | 4 Department of Neurology Medical University of Graz Graz Austria 6 Department of Medical Physics and Biomedical Engineering University College London London UK 3 Millennium Institute for Intelligent Healthcare Engineering (iHEALTH) Santiago Chile 5 BioTechMed Graz Graz Austria 2 Biomedical Imaging Center Pontificia Universidad Catolica de Chile Santiago Chile 1 Department of Electrical Engineering Pontificia Universidad Catolica de Chile Santiago Chile |
| AuthorAffiliation_xml | – name: 1 Department of Electrical Engineering Pontificia Universidad Catolica de Chile Santiago Chile – name: 4 Department of Neurology Medical University of Graz Graz Austria – name: 5 BioTechMed Graz Graz Austria – name: 6 Department of Medical Physics and Biomedical Engineering University College London London UK – name: 2 Biomedical Imaging Center Pontificia Universidad Catolica de Chile Santiago Chile – name: 3 Millennium Institute for Intelligent Healthcare Engineering (iHEALTH) Santiago Chile |
| Author_xml | – sequence: 1 givenname: Mathias orcidid: 0000-0002-2996-8141 surname: Lambert fullname: Lambert, Mathias email: mglambert@uc.cl organization: Millennium Institute for Intelligent Healthcare Engineering (iHEALTH) – sequence: 2 givenname: Cristian surname: Tejos fullname: Tejos, Cristian organization: Millennium Institute for Intelligent Healthcare Engineering (iHEALTH) – sequence: 3 givenname: Christian orcidid: 0000-0002-7097-9707 surname: Langkammer fullname: Langkammer, Christian organization: BioTechMed Graz – sequence: 4 givenname: Carlos orcidid: 0000-0002-1196-6703 surname: Milovic fullname: Milovic, Carlos organization: University College London |
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| Cites_doi | 10.1002/mrm.22135 10.1148/radiol.12120707 10.1109/TMI.2009.2023787 10.1002/cmr.b.10083 10.1016/j.neuroimage.2012.05.049 10.1109/TMI.2010.2090538 10.1016/j.mri.2019.08.028 10.1002/mrm.21710 10.1016/j.mri.2014.09.004 10.1561/2200000016 10.1371/journal.pone.0162460 10.1002/jmri.22276 10.1002/mrm.28716 10.1002/mrm.21828 10.1002/mrm.28754 10.3174/ajnr.A4617 10.1002/jmri.24644 10.1093/brain/aww278 10.1002/mrm.28957 10.1002/cmr.a.20124 10.1109/TMI.2018.2884093 10.1002/nbm.3604 10.1002/mrm.22187 10.1038/jcbfm.2011.118 10.1371/journal.pone.0081093 10.1002/mrm.24272 10.1117/12.2188535 10.1109/TIP.2011.2172801 10.1002/mrm.27483 10.1002/mrm.1910340618 10.1002/nbm.3601 10.1002/cmr.b.20034 10.1002/mrm.28435 10.1002/mrm.26830 10.1002/mrm.27073 10.1002/nbm.1670 |
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Susceptibility maps are usually derived from local magnetic field estimations by minimizing a functional composed of a data consistency term and a... Susceptibility maps are usually derived from local magnetic field estimations by minimizing a functional composed of a data consistency term and a... PurposeSusceptibility maps are usually derived from local magnetic field estimations by minimizing a functional composed of a data consistency term and a... |
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| SubjectTerms | Accuracy Augmented Lagrangian Computer applications Consistency L1‐norm L2‐norm Magnetic resonance imaging Noise reduction Norms Outliers (statistics) QSM QSM challenge Regularization Technical Note Technical Note–Computer Processing and Modeling |
| Title | Hybrid data fidelity term approach for quantitative susceptibility mapping |
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