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Improved Susceptibility Artifact Correction of Echo-Planar MRI using the Alternating Direction Method of Multipliers

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Abstract

We present an improved technique for susceptibility artifact correction in echo-planar imaging (EPI), a widely used ultra-fast magnetic resonance imaging (MRI) technique. Our method corrects geometric deformations and intensity modulations present in EPI images. We consider a tailored variational image registration problem incorporating a physical distortion model and aiming at minimizing the distance of two oppositely distorted images subject to invertibility constraints. We derive a novel face-staggered discretization of the variational problem that renders the discretized distance function and constraints separable. Motivated by the presence of a smoothness regularizer, which leads to global coupling, we apply the alternating direction method of multipliers (ADMM) to split the problem into simpler subproblems. We prove the convergence of ADMM for this non-convex optimization problem. We show the superiority of our scheme compared to two state-of-the-art methods both in terms of correction quality and time-to-solution for 13 high-resolution 3D imaging datasets.

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Acknowledgements

The 3D data are provided by the Human Connectome Project, WU-Minn Consortium (PIs: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research and by the McDonnell Center for Systems Neuroscience at Washington University. We also like to thank Siawoosh Mohammadi (University Hospital Hamburg Eppendorf, Germany) and Harald Kugel (Department of Clinical Radiology, University Hospital Münster, Germany) for fruitful discussions and helpful suggestions on a first draft of this manuscript. This work is partially supported by the National Science Foundation (NSF) award DMS 1522599.

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Authors and Affiliations

  1. Technische Universität Berlin, Berlin, Germany

    Jan Macdonald

  2. Emory University, Atlanta, GA, USA

    Lars Ruthotto

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  1. Jan Macdonald
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  2. Lars Ruthotto
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Correspondence to Lars Ruthotto.

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The second author’s work is supported in part by National Science Foundation (NSF) grant DMS 1522599.

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Macdonald, J., Ruthotto, L. Improved Susceptibility Artifact Correction of Echo-Planar MRI using the Alternating Direction Method of Multipliers. J Math Imaging Vis 60, 268–282 (2018). https://doi.org/10.1007/s10851-017-0757-x

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  • DOI: https://doi.org/10.1007/s10851-017-0757-x

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