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TERNARY QUARTIC APPROACH FOR POSITIVE 4TH ORDER DIFFUSION TENSORS REVISITED

Aurobrata Ghosh 1 Rachid Deriche 1 Maher Moakher 2
1 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique de l'École normale supérieure, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : In Diffusion Magnetic Resonance Imaging (D-MRI), the 2nd order diffusion tensor has given rise to a widely used tool – Diffusion Tensor Imaging (DTI). However, it is known that DTI is limited to a single prominent diffusion direction and is inaccurate in regions of complex fiber structures such as crossings. Various other approaches have been introduced to recover such complex tissue micro-geometries, one of which is Higher Order Cartesian Tensors. Estimating a positive diffusion function has also been emphasised mathematically, since diffusion is a physical quantity. Recently there have been efforts to estimate 4th order diffusion tensors from DiffusionWeighted Images (DWIs), which are capable of describing crossing configurations with the added property of a positive diffusion function. We take up one such, the Ternary Quartic approach, and reformulate the estimation equation to facilitate the estimation of the non-negative 4th order diffusion tensor. With our modified approach we test on synthetic, phantom and real data and confirm previous results.
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https://hal.inria.fr/inria-00496873
Contributor : Aurobrata Ghosh <>
Submitted on : Thursday, July 1, 2010 - 3:30:21 PM
Last modification on : Thursday, July 1, 2021 - 5:58:03 PM
Long-term archiving on: : Monday, October 4, 2010 - 12:00:01 PM

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Aurobrata Ghosh, Rachid Deriche, Maher Moakher. TERNARY QUARTIC APPROACH FOR POSITIVE 4TH ORDER DIFFUSION TENSORS REVISITED. 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Jun 2009, Boston, United States. 4 p. ⟨inria-00496873⟩

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