D-eigenvalues of diffusion kurtosis tensors

Authors:
Liqun Qi;Yiju Wang;Ed X. Wu
Affiliations:
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;School of Operations Research and Management Sciences, Qufu Normal University, Rizhao Shandong, 276800, China;Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 4
Cited 8

Mathematics for computer algebra

Mathematics for computer algebra
Rank and eigenvalues of a supersymmetric tensor, the multivariate homogeneous polynomial and the algebraic hypersurface it defines

Journal of Symbolic Computation
Z-eigenvalue methods for a global polynomial optimization problem

Mathematical Programming: Series A and B
Eigenvalues of a real supersymmetric tensor

Journal of Symbolic Computation

Extreme diffusion values for non-Gaussian diffusions

Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART I
An always convergent algorithm for the largest eigenvalue of an irreducible nonnegative tensor

Journal of Computational and Applied Mathematics
Finding the Largest Eigenvalue of a Nonnegative Tensor

SIAM Journal on Matrix Analysis and Applications
Higher Order Positive Semidefinite Diffusion Tensor Imaging

SIAM Journal on Imaging Sciences
Further Results for Perron-Frobenius Theorem for Nonnegative Tensors

SIAM Journal on Matrix Analysis and Applications
Gradient skewness tensors and local illumination detection for images

Journal of Computational and Applied Mathematics
Nonnegative Diffusion Orientation Distribution Function

Journal of Mathematical Imaging and Vision
Criterions for the positive definiteness of real supersymmetric tensors

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.30

Visualization

Abstract

Diffusion kurtosis imaging (DKI) is a new model in medical engineering, where a diffusion kurtosis (DK) tensor is involved. A DK tensor is a fourth-order three-dimensional fully symmetric tensor. In this paper, we introduce D-eigenvalues for a DK tensor. The largest, the smallest and the average D-eigenvalues of a DK tensor correspond with the largest, the smallest and the average apparent kurtosis coefficients (AKC) of a water molecule in the space, respectively. We present their computational methods and discuss related anisotropy value of AKC.