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Computational Diffusion MRI pp 131–143Cite as

Adaptive Enhancement in Diffusion MRI Through Propagator Sharpening

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

Abstract

In this short note we consider a method of enhancing diffusion MRI data based on analytically deblurring the ensemble average propagator. Because of the Fourier relationship between the normalized signal and the propagator, this technique can be applied in a straightforward manner to a large class of models. In the case of diffusion tensor imaging, a commonly used ‘ad hoc’ \(\min\)-normalization sharpening method is shown to be closely related to this deblurring approach. The main goal of this manuscript is to give a formal description of the method for (generalized) diffusion tensor imaging and higher order apparent diffusion coefficient-based models. We also show how the method can be made adaptive to the data, and present the effect of our proposed enhancement on scalar maps and tractography output.

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Notes

  1. 1.

    We assume a standard pulsed gradient spin echo sequence.

  2. 2.

    This follows from Eq. (1) under some regularity conditions.

  3. 3.

    http://bmia.bmt.tue.nl/software/viste/.

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Acknowledgements

Tom Dela Haije gratefully acknowledges The Netherlands Organisation for Scientific Research (NWO) for financial support. Neda Sepasian and Tom Dela Haije are equal first authors.

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Authors and Affiliations

  1. Eindhoven University of Technology, Den Dolech 2, 513, 5600MB, Eindhoven, Noord-Brabant, The Netherlands

    Tom Dela Haije, Neda Sepasian, Andrea Fuster & Luc Florack

Authors
  1. Tom Dela Haije
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  2. Neda Sepasian
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  3. Andrea Fuster
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  4. Luc Florack
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Corresponding author

Correspondence to Tom Dela Haije .

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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Dela Haije, T., Sepasian, N., Fuster, A., Florack, L. (2016). Adaptive Enhancement in Diffusion MRI Through Propagator Sharpening. 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_12

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