A New Tensorial Framework for Single-Shell High Angular Resolution Diffusion Imaging

Authors:
Luc Florack;Evgeniya Balmashnova;Laura Astola;Ellen Brunenberg
Affiliations:
Department of Mathematics & Computer Science and Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands;Department of Mathematics & Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands;Department of Mathematics & Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands;Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
Venue:
Journal of Mathematical Imaging and Vision
Year:
2010

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Abstract

Single-shell high angular resolution diffusion imaging data (HARDI) may be decomposed into a sum of eigenpolynomials of the Laplace-Beltrami operator on the unit sphere. The resulting representation combines the strengths hitherto offered by higher order tensor decomposition in a tensorial framework and spherical harmonic expansion in an analytical framework, but removes some of the conceptual weaknesses of either. In particular it admits analytically closed form expressions for Tikhonov regularization schemes and estimation of an orientation distribution function via the Funk-Radon Transform in tensorial form, which previously required recourse to spherical harmonic decomposition. As such it provides a natural point of departure for a Riemann-Finsler extension of the geometric approach towards tractography and connectivity analysis as has been stipulated in the context of diffusion tensor imaging (DTI), while at the same time retaining the natural coarse-to-fine hierarchy intrinsic to spherical harmonic decomposition.