Volume 6, Issue 1
Numerical Schemes for Linear and Non-Linear Enhancement of DW-MRI

Eric Creusen, Remco Duits, Anna Vilanova & Luc Florack

Numer. Math. Theor. Meth. Appl., 6 (2013), pp. 138-168.

Published online: 2013-06

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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 numerical schemes.

  • Keywords

DTI, DW-MRI, scale spaces, finite differences, convection-diffusion, adaptive diffusion, Perona-Malik diffusion, Lie groups.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-6-138, author = {}, title = {Numerical Schemes for Linear and Non-Linear Enhancement of DW-MRI}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2013}, volume = {6}, number = {1}, pages = {138--168}, 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 numerical schemes.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2013.mssvm08}, url = {http://global-sci.org/intro/article_detail/nmtma/5898.html} }
TY - JOUR T1 - Numerical Schemes for Linear and Non-Linear Enhancement of DW-MRI JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 138 EP - 168 PY - 2013 DA - 2013/06 SN - 6 DO - http://doi.org/10.4208/nmtma.2013.mssvm08 UR - https://global-sci.org/intro/article_detail/nmtma/5898.html KW - DTI, DW-MRI, scale spaces, finite differences, convection-diffusion, adaptive diffusion, Perona-Malik diffusion, Lie groups. AB -

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 numerical schemes.

Eric Creusen, Remco Duits, Anna Vilanova & Luc Florack. (2020). Numerical Schemes for Linear and Non-Linear Enhancement of DW-MRI. Numerical Mathematics: Theory, Methods and Applications. 6 (1). 138-168. doi:10.4208/nmtma.2013.mssvm08
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