Estimation of integral curves from high angular resolution diffusion imaging (HARDI) data

Owen Carmichael, Lyudmila Sakhanenko

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We develop statistical methodology for a popular brain imaging technique HARDI based on the high order tensor model by Özarslan and Mareci [10]. We investigate how uncertainty in the imaging procedure propagates through all levels of the model: signals, tensor fields, vector fields, and fibers. We construct asymptotically normal estimators of the integral curves or fibers which allow us to trace the fibers together with confidence ellipsoids. The procedure is computationally intense as it blends linear algebra concepts from high order tensors with asymptotical statistical analysis. The theoretical results are illustrated on simulated and real datasets. This work generalizes the statistical methodology proposed for low angular resolution diffusion tensor imaging by Carmichael and Sakhanenko [3], to several fibers per voxel. It is also a pioneering statistical work on tractography from HARDI data. It avoids all the typical limitations of the deterministic tractography methods and it delivers the same information as probabilistic tractography methods. Our method is computationally cheap and it provides well-founded mathematical and statistical framework where diverse functionals on fibers, directions and tensors can be studied in a systematic and rigorous way.

Original languageEnglish (US)
Pages (from-to)377-403
Number of pages27
JournalLinear Algebra and Its Applications
Volume473
DOIs
StatePublished - May 15 2015

Fingerprint

High Angular Resolution
Imaging
Fiber
Tensors
Imaging techniques
Curve
Higher-order Tensor
Fibers
Tensor
Diffusion tensor imaging
Linear algebra
Methodology
Probabilistic Methods
Voxel
Ellipsoid
Statistical Analysis
Confidence
Brain
Vector Field
Statistical methods

Keywords

  • Asymptotic normality
  • Diffusion tensor imaging
  • Integral curve
  • Kernel smoothing

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics
  • Geometry and Topology
  • Numerical Analysis

Cite this

Estimation of integral curves from high angular resolution diffusion imaging (HARDI) data. / Carmichael, Owen; Sakhanenko, Lyudmila.

In: Linear Algebra and Its Applications, Vol. 473, 15.05.2015, p. 377-403.

Research output: Contribution to journalArticle

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