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Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging. (English) Zbl 1196.62063

Summary: The statistical analysis of covariance matrix data is considered and, in particular a methodology is discussed which takes into account the non-Euclidean nature of the space of positive semi-definite symmetric matrices. The main motivation for this work is the analysis of diffusion tensors in medical image analysis. The primary focus is on estimation of a mean covariance matrix and, in particular, on the use of a Procrustes size-and-shape space. Comparisons are made with other estimation techniques, including using the matrix logarithm, matrix square root and Cholesky decomposition. Applications to diffusion tensor imaging are considered and, in particular, a new measure of fractional anisotropy called Procrustes anisotropy is discussed.

MSC:

62H12 Estimation in multivariate analysis
62H35 Image analysis in multivariate analysis
92C55 Biomedical imaging and signal processing
65C60 Computational problems in statistics (MSC2010)

Software:

R
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References:

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