Extreme diffusion values for non-Gaussian diffusions

Authors:
Deren Han;Liqun Qi;X. Wu
Affiliations:
Institute of Mathematics, School of Mathematics and Computer Science, Nanjing Normal University, Nanjing, Jiangsu, PR China;Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong
Venue:
Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART I
Year:
2008

Citing 4
Cited 1

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

Journal of Symbolic Computation
D-eigenvalues of diffusion kurtosis tensors

Journal of Computational and Applied Mathematics
Eigenvalues of a real supersymmetric tensor

Journal of Symbolic Computation
Symmetric positive 4th order tensors & their estimation from diffusion weighted MRI

IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging

Approximating Symmetric Positive Semidefinite Tensors of Even Order

SIAM Journal on Imaging Sciences

Quantified Score

Hi-index	0.00

Visualization

Abstract

A new magnetic resonance imaging (MRI) model, called diffusion kurtosis imaging (DKI), was recently proposed, to characterize the non-Gaussian diffusion behaviour in tissues. DKI involves a fourth-order three-dimensional tensor and a second-order three-dimensional tensor. Similar to those in the diffusion tensor imaging (DTI) model, the extreme diffusion values and extreme directions associated to this tensor pair play important roles in DKI. In this paper, we study the properties of the extreme values and directions associated to such tensor pairs. We also present a numerical method and its preliminary computational results.