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Journal article
Regularized positive-definite fourth order tensor field estimation from DW-MRI
NeuroImage (Orlando, Fla.), v 45(1), pp S153-S162
01 Mar 2009
PMID: 19063978
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Abstract
In Diffusion Weighted Magnetic Resonance Image (DW-MRI) processing, a 2nd order tensor has been commonly used to approximate the diffusivity function at each lattice point of the DW-MRI data. From this tensor approximation, one can compute useful scalar quantities (e. g. anisotropy, mean diffusivity) which have been clinically used for monitoring encephalopathy, sclerosis, ischemia and other brain disorders. It is now well known that this 2nd-order tensor approximation fails to capture complex local tissue structures, e. g. crossing fibers, and as a result, the scalar quantities derived from these tensors are grossly inaccurate at such locations. In this paper we employ a 4th order symmetric positive-definite (SPD) tensor approximation to represent the diffusivity function and present a novel technique to estimate these tensors from the DW-MRI data guaranteeing the SPD property. Several articles have been reported in literature on higher order tensor approximations of the diffusivity function but none of them guarantee the positivity of the estimates, which is a fundamental constraint since negative values of the diffusivity are not meaningful. In this paper we represent the 4th-order tensors as ternary quartics and then apply Hilbert's theorem on ternary quartics along with the Iwasawa parametrization to guarantee an SPD 4th-order tensor approximation from the DW-MRI data. The performance of this model is depicted on synthetic data as well as real DW-MRIs from a set of excised control and injured rat spinal cords, showing accurate estimation of scalar quantities such as generalized anisotropy and trace as well as fiber orientations. (C) 2008 Elsevier Inc. All rights reserved.
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Details
- Title
- Regularized positive-definite fourth order tensor field estimation from DW-MRI
- Creators
- Angelos Barmpoutis - University of FloridaMin Sig Hwang - University of FloridaDena Howland - University of FloridaJohn R. Forder - University of FloridaBaba C. Vemuri - University of Florida
- Publication Details
- NeuroImage (Orlando, Fla.), v 45(1), pp S153-S162
- Publisher
- Elsevier
- Number of pages
- 10
- Grant note
- R01 EB007082-03; R01 EB007082; R01 EB007082-04; EB007082 / NIBIB NIH HHS; United States Department of Health & Human Services; National Institutes of Health (NIH) - USA; NIH National Institute of Biomedical Imaging & Bioengineering (NIBIB) R01EB007082 / NATIONAL INSTITUTE OF BIOMEDICAL IMAGING AND BIOENGINEERING; United States Department of Health & Human Services; National Institutes of Health (NIH) - USA; NIH National Institute of Biomedical Imaging & Bioengineering (NIBIB)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Radiation Oncology (and Nuclear Medicine)
- Web of Science ID
- WOS:000263862600014
- Scopus ID
- 2-s2.0-65549135890
- Other Identifier
- 991021897485704721
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InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Neuroimaging
- Neurosciences
- Radiology, Nuclear Medicine & Medical Imaging