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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


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 / Florian Knoll
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, Volume 21, Issue 3, Pages 355–377, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jip-2013-0005.

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