Regularisation, interpolation and visualisation of diffusion tensor images using non-Euclidean statistics.

Zhou, Diwei and Dryden, Ian L. and Koloydenko, Alexey A. and Audenaert, Koenraad M.R. and Bai, Li (2016) Regularisation, interpolation and visualisation of diffusion tensor images using non-Euclidean statistics. Journal of Applied Statistics, 43 (5). pp. 943-978. ISSN 1360-0532

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Practical statistical analysis of diffusion tensor images is considered, and we focus primarily on methods that use metrics based on Euclidean distances between powers of diffusion tensors. First we describe a family of anisotropy measures based on a scale invariant power-Euclidean metric, which are useful for visualisation. Some properties of the measures are derived and practical considerations are discussed, with some examples. Second we discuss weighted Procrustes methods for diffusion tensor interpolation and smoothing, and we compare methods based on different metrics on a set of examples as well as analytically. We establish a key relationship between the principal-square-root-Euclidean metric and the size-and-shape Procrustes metric on the space of symmetric positive semi-definite tensors. We explain, both analytically and by experiments, why the size-and-shape Procrustes metric may be preferred in practical tasks of interpolation, extrapolation, and smoothing, especially when observed tensors are degenerate or when a moderate degree of tensor swelling is desirable. Third we introduce regularisation methodology, which is demonstrated to be useful for highlighting features of prior interest and potentially for segmentation. Finally, we compare several metrics in a dataset of human brain diffusion-weighted MRI, and point out similarities between several of the non-Euclidean metrics but important differences with the commonly used Euclidean metric.

Item Type: Article
Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis Group in Journal of Applied Statistics on 23/09/2015, available online:
Keywords: Anisotropy; Metric; Positive definite; Power; Procrustes; Riemannian; Smoothing; Weighted Frechet mean
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1080/02664763.2015.1080671
Depositing User: Dryden, Professor Ian
Date Deposited: 09 Mar 2017 09:55
Last Modified: 19 Mar 2017 10:08

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