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Title: Regularisation, interpolation and visualisation of diffusion tensor images using non-Euclidean statistics
Authors: Zhou, Diwei
Dryden, Ian L.
Koloydenko, Alexey
Audenaert, K.M.R.
Bai, Li
Keywords: Anisotropy
Positive definite
Weighted Frechet mean
Issue Date: 2016
Publisher: © Taylor & Francis
Citation: ZHOU, D. ...et al., 2016. Regularisation, interpolation and visualisation of diffusion tensor images using non-Euclidean statistics. Journal of Applied Statistics 43(5), pp.943-978.
Abstract: 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 visualization. Some properties of the measures are derived and practical considerations are discussed, with some examples. Second we discuss weighted Procrustes methods for DTI 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.
Description: This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Applied Statistics on 23rd September 2015, available online: http://dx.doi.org/10.1080/02664763.2015.1080671
Sponsor: The second author acknowledges support from a Royal Society Wolfson Research Merit Award and EPSRC grant EP/K022547/1.
Version: Accepted for publication
DOI: 10.1080/02664763.2015.1080671
URI: https://dspace.lboro.ac.uk/2134/18801
Publisher Link: http://dx.doi.org/10.1080/02664763.2015.1080671
Appears in Collections:Published Articles (Maths)

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