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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 21, Issue 3 (Jun 2013)


TGV for diffusion tensors: A comparison of fidelity functions

Tuomo Valkonen
  • Institute for Mathematics and Scientific Computing, University of Graz, Austria. Current address: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, United Kingdom
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/ Kristian Bredies
  • Institute for Mathematics and Scientific Computing, University of Graz, Austria
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/ Florian Knoll
  • Institute of Medical Engineering, Graz University of Technology, Austria
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Published Online: 2013-06-05 | DOI: https://doi.org/10.1515/jip-2013-0005


We study the total generalised variation regularisation of symmetric tensor fields from medical applications, namely diffusion tensor regularisation. We study the effect of the pointwise positivity constraint on the tensor field, as well as the difference between direct denoising of the tensor field first solved from the Stejskal–Tanner equation, as was done in our earlier work, and of incorporating this equation into the fidelity function. Our results indicate that the latter novel approach provides improved computational results.

Keywords: Total generalised variation; total deformation; regularisation; diffusion tensor imaging; medical imaging

About the article

Received: 2012-10-01

Published Online: 2013-06-05

Published in Print: 2013-06-01

Citation Information: Journal of Inverse and Ill-Posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jip-2013-0005.

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© 2013 by Walter de Gruyter Berlin Boston. Copyright Clearance Center

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