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Numerical Schemes for Linear and Non-Linear Enhancement of DW-MRI

Published online by Cambridge University Press:  28 May 2015

Eric Creusen ,
Remco Duits ,
Anna Vilanova  and
Luc Florack
Eric Creusen*
Affiliation:
Department of Mathematics and Computer Science, CASA Applied Analysis, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
Remco Duits*
Affiliation:
Department of Mathematics and Computer Science, CASA Applied Analysis, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands Department of Biomedical Engineering, BMIA Biomedical Image Analysis, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
Anna Vilanova
Affiliation:
Department of Biomedical Engineering, BMIA Biomedical Image Analysis, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
Luc Florack
Affiliation:
Department of Mathematics and Computer Science, CASA Applied Analysis, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands Department of Biomedical Engineering, BMIA Biomedical Image Analysis, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
*
Corresponding author.Email address:e.j.creusen@tue.nl
Corresponding author.Email address:r.duits@tue.nl
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Abstract

We consider the linear and non-linear enhancement of diffusion weighted magnetic resonance images (DW-MRI) to use contextual information in denoising and inferring fiber crossings. We describe the space of DW-MRI images in a moving frame of reference, attached to fiber fragments which allows for convection-diffusion along the fibers. Because of this approach, our method is naturally able to handle crossings in data. We will perform experiments showing the ability of the enhancement to infer information about crossing structures, even in diffusion tensor images (DTI) which are incapable of representing crossings themselves. We will present a novel non-linear enhancement technique which performs better than linear methods in areas around ventricles, thereby eliminating the need for additional preprocessing steps to segment out the ventricles. We pay special attention to the details of implementation of the various numeric schemes.

Keywords

65M1078A48DTIDW-MRIscale spacesfinite differencesconvection-diffusionadaptive diffusionPerona-Malik diffusionLie groups
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 1 , February 2013 , pp. 138 - 168
Copyright
Copyright © Global Science Press Limited 2013

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