Detection of Crossing White Matter Fibers with High-Order Tensors and Rank-k Decompositions

Fangxiang Jiao; Yaniv Gur; Chris R. Johnson; Sarang Joshi

doi:10.1007/978-3-642-22092-0_44

Detection of Crossing White Matter Fibers with High-Order Tensors and Rank-k Decompositions

Fangxiang Jiao, Yaniv Gur, Chris R. Johnson, Sarang Joshi

Research output: Chapter in Book/Report/Conference proceeding › Chapter

24 Scopus citations

Abstract

Fundamental to high angular resolution diffusion imaging (HARDI), is the estimation of a positive-semidefinite orientation distribution function (ODF) and extracting the diffusion properties (e.g., fiber directions). In this work we show that these two goals can be achieved efficiently by using homogeneous polynomials to represent the ODF in the spherical deconvolution approach, as was proposed in the Cartesian Tensor-ODF (CT-ODF) formulation. Based on this formulation we first suggest an estimation method for positive-semidefinite ODF by solving a linear programming problem that does not require special parameterization of the ODF. We also propose a rank-k tensor decomposition, known as CP decomposition, to extract the fibers information from the estimated ODF. We show that this decomposition is superior to the fiber direction estimation via ODF maxima detection as it enables one to reach the full fiber separation resolution of the estimation technique. We assess the accuracy of this new framework by applying it to synthetic and experimentally obtained HARDI data. © 2011 Springer-Verlag.

Original language	English (US)
Title of host publication	Information Processing in Medical Imaging
Publisher	Springer Nature
Pages	538-549
Number of pages	12
ISBN (Print)	9783642220913
DOIs	https://doi.org/10.1007/978-3-642-22092-0_44
State	Published - 2011
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The authors would like to thank Tamara G. Kolda of San-dia National Labs, Livermore, California, for useful discussions and comments re-garding this work. This research wasfunded by the NIH grants: 5R01EB007688,5R01HL092055, and by the NIH/NCRR Center for Integrative Biomedical Com-puting, P41-RR12553-10, Award No. KUS-C1-016-04, made by King AbdullahUniversity of Science and Technology (KAUST), and DOE SciDAC VACET.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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title = "Detection of Crossing White Matter Fibers with High-Order Tensors and Rank-k Decompositions",

abstract = "Fundamental to high angular resolution diffusion imaging (HARDI), is the estimation of a positive-semidefinite orientation distribution function (ODF) and extracting the diffusion properties (e.g., fiber directions). In this work we show that these two goals can be achieved efficiently by using homogeneous polynomials to represent the ODF in the spherical deconvolution approach, as was proposed in the Cartesian Tensor-ODF (CT-ODF) formulation. Based on this formulation we first suggest an estimation method for positive-semidefinite ODF by solving a linear programming problem that does not require special parameterization of the ODF. We also propose a rank-k tensor decomposition, known as CP decomposition, to extract the fibers information from the estimated ODF. We show that this decomposition is superior to the fiber direction estimation via ODF maxima detection as it enables one to reach the full fiber separation resolution of the estimation technique. We assess the accuracy of this new framework by applying it to synthetic and experimentally obtained HARDI data. {\textcopyright} 2011 Springer-Verlag.",

author = "Fangxiang Jiao and Yaniv Gur and Johnson, {Chris R.} and Sarang Joshi",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: The authors would like to thank Tamara G. Kolda of San-dia National Labs, Livermore, California, for useful discussions and comments re-garding this work. This research wasfunded by the NIH grants: 5R01EB007688,5R01HL092055, and by the NIH/NCRR Center for Integrative Biomedical Com-puting, P41-RR12553-10, Award No. KUS-C1-016-04, made by King AbdullahUniversity of Science and Technology (KAUST), and DOE SciDAC VACET. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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AU - Gur, Yaniv

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AU - Joshi, Sarang

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: The authors would like to thank Tamara G. Kolda of San-dia National Labs, Livermore, California, for useful discussions and comments re-garding this work. This research wasfunded by the NIH grants: 5R01EB007688,5R01HL092055, and by the NIH/NCRR Center for Integrative Biomedical Com-puting, P41-RR12553-10, Award No. KUS-C1-016-04, made by King AbdullahUniversity of Science and Technology (KAUST), and DOE SciDAC VACET. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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N2 - Fundamental to high angular resolution diffusion imaging (HARDI), is the estimation of a positive-semidefinite orientation distribution function (ODF) and extracting the diffusion properties (e.g., fiber directions). In this work we show that these two goals can be achieved efficiently by using homogeneous polynomials to represent the ODF in the spherical deconvolution approach, as was proposed in the Cartesian Tensor-ODF (CT-ODF) formulation. Based on this formulation we first suggest an estimation method for positive-semidefinite ODF by solving a linear programming problem that does not require special parameterization of the ODF. We also propose a rank-k tensor decomposition, known as CP decomposition, to extract the fibers information from the estimated ODF. We show that this decomposition is superior to the fiber direction estimation via ODF maxima detection as it enables one to reach the full fiber separation resolution of the estimation technique. We assess the accuracy of this new framework by applying it to synthetic and experimentally obtained HARDI data. © 2011 Springer-Verlag.

AB - Fundamental to high angular resolution diffusion imaging (HARDI), is the estimation of a positive-semidefinite orientation distribution function (ODF) and extracting the diffusion properties (e.g., fiber directions). In this work we show that these two goals can be achieved efficiently by using homogeneous polynomials to represent the ODF in the spherical deconvolution approach, as was proposed in the Cartesian Tensor-ODF (CT-ODF) formulation. Based on this formulation we first suggest an estimation method for positive-semidefinite ODF by solving a linear programming problem that does not require special parameterization of the ODF. We also propose a rank-k tensor decomposition, known as CP decomposition, to extract the fibers information from the estimated ODF. We show that this decomposition is superior to the fiber direction estimation via ODF maxima detection as it enables one to reach the full fiber separation resolution of the estimation technique. We assess the accuracy of this new framework by applying it to synthetic and experimentally obtained HARDI data. © 2011 Springer-Verlag.

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ER -

Detection of Crossing White Matter Fibers with High-Order Tensors and Rank-k Decompositions

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