Higher Order Diffusion Tensor Imaging

  • Liqun Qi
  • Haibin Chen
  • Yannan Chen
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 39)


Diffusion tensor imaging (DTI) is one of the most promising medical imaging models, and the most applicable technique in modern clinical medicine. While, there are limitations to DTI, which becomes useless in non-isotropic materials. As a resolution, diffusion kurtosis imaging (DKI) is proposed as a new model in medical engineering, which can characterize the non-Gaussian diffusion behavior in tissues, and in which a diffusion kurtosis (DK) tensor is involved. A DK tensor is a fourth order three dimensional symmetric tensor. In this chapter, we will apply the spectral theory of tensors to this particular type of tensors arising from medical imaging and derive some applications.

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Applied MathematicsThe Hong Kong Polytechnic University Hong KongHong Kong
  2. 2.School of Management Sciences Qufu Normal UniversityRizhaoChina
  3. 3.The Hong Kong Polytechnic University Hong KongHong Kong

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