Higher-order tensors in diffusion imaging

T. Schultz, A. Fuster, A. Ghosh, R. Deriche, L.M.J. Florack, L.H. Lim

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureHoofdstukAcademic

14 Citaten (Scopus)
4 Downloads (Pure)

Samenvatting

Diffusion imaging is a noninvasive tool for probing the microstructure of fibrous nerve and muscle tissue. Higher-order tensors provide a powerful mathematical language to model and analyze the large and complex data that is generated by its modern variants such as High Angular Resolution Diffusion Imaging (HARDI) or Diffusional Kurtosis Imaging. This survey gives a careful introduction to the foundations of higher-order tensor algebra, and explains how some concepts from linear algebra generalize to the higher-order case. From the application side, it reviews a variety of distinct higher-order tensor models that arise in the context of diffusion imaging, such as higher-order diffusion tensors, q-ball or fiber Orientation Distribution Functions (ODFs), and fourth-order covariance and kurtosis tensors. By bridging the gap between mathematical foundations and application, it provides an introduction that is suitable for practitioners and applied mathematicians alike, and propels the field by stimulating further exchange between the two.
Originele taal-2Engels
TitelVisualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data, Part III
RedacteurenC.-F. Westin, A. Vilanova, B. Burgeth
UitgeverijSpringer
Pagina's129-161
ISBN van geprinte versie978-3-642-54300-5
DOI's
StatusGepubliceerd - 2014

Publicatie series

NaamMathematics and Visualization
ISSN van geprinte versie1612-3786

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  • Citeer dit

    Schultz, T., Fuster, A., Ghosh, A., Deriche, R., Florack, L. M. J., & Lim, L. H. (2014). Higher-order tensors in diffusion imaging. In C-F. Westin, A. Vilanova, & B. Burgeth (editors), Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data, Part III (blz. 129-161). (Mathematics and Visualization). Springer. https://doi.org/10.1007/978-3-642-54301-2_6