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Computational Diffusion MRI pp 27–39Cite as

Holistic Image Reconstruction for Diffusion MRI

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Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

Diffusion MRI provides unique information on the microarchitecture of biological tissues. One of the major challenges is finding a balance between image resolution, acquisition duration, noise level and image artifacts. Recent methods tackle this challenge by performing super-resolution reconstruction in image space or in diffusion space, regularization of the image data or of postprocessed data (such as the orientation distribution function, ODF) along different dimensions, and/or impose data-consistency in the original acquisition space. Each of these techniques has its own advantages; however, it is rare that even a few of them are combined. Here we present a holistic framework for diffusion MRI reconstruction that allows combining the advantages of all these techniques in a single reconstruction step. In proof-of-concept experiments, we demonstrate super-resolution on HARDI shells and in image space, regularization of the ODF and of the images in spatial and angular dimensions, and data consistency in the original acquisition space. Reconstruction quality is superior to standard reconstruction, demonstrating the feasibility of combining advanced techniques into one step.

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Notes

  1. 1.

    The ODF is a formalism that characterizes the strength of diffusion in different directions. It is defined formally below in Eq. (10).

  2. 2.

    The precise formula that we use for R(r) will follow later in Eq. (12).

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Acknowledgements

V.G. is supported by the Deutsche Telekom Foundation. The research leading to the results of this article has received funding from the European Research Council under the ECs 7th Framework Programme (FP7/2007-2014)/ERC grant agr. no. 335555. Data were provided by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: 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.

Author information

Authors and Affiliations

  1. Department of Informatics, Technische Universität München, Garching, Germany

    Vladimir Golkov & Daniel Cremers

  2. Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands

    Jorg M. Portegies

  3. Department of Mathematics, Augsburg University, Augsburg, Germany

    Antonij Golkov

  4. Department of Mathematics and Computer Science, and Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Remco Duits

Authors
  1. Vladimir Golkov
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  2. Jorg M. Portegies
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  3. Antonij Golkov
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  4. Remco Duits
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  5. Daniel Cremers
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Corresponding author

Correspondence to Vladimir Golkov .

Editor information

Editors and Affiliations

  1. Dept of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands

    Andrea Fuster

  2. Centre for Medical Image Computing, University College London, London, United Kingdom

    Aurobrata Ghosh

  3. Centre for Medical Image Computing, University College London, London, United Kingdom

    Enrico Kaden

  4. Brigham and Women's Hospital, Harvard Medical School, Boston, Massachusetts, USA

    Yogesh Rathi

  5. Department of Radiology, University Medical Center, Freiburg, Germany

    Marco Reisert

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© 2016 Springer International Publishing Switzerland

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Golkov, V., Portegies, J.M., Golkov, A., Duits, R., Cremers, D. (2016). Holistic Image Reconstruction for Diffusion MRI. In: Fuster, A., Ghosh, A., Kaden, E., Rathi, Y., Reisert, M. (eds) Computational Diffusion MRI. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-28588-7_3

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