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Non-parametric estimation of HARDI diffusion weighted magnetic resonance imaging data

Thursday 6th March 2008 - 11:00 to 12:00
INI Seminar Room 1

Diffusion-Weighted Magnetic Resonance Imaging captures the diffusion of water molecules in tissue. The impediment of this diffusion process by nerves enables the characterisation of white matter structure and the measurement of quantitative descriptions of white matter integrity.

Initial quantification of the diffusion was based on modelling the Diffusion PDF parametrically, and as such the parameters of the PDF can be estimated, if with some model-choice issues. A single Gaussian Diffusion Tensor model can for example be determined with a minimum of 6 measurements. Of special interest is inferring the orientational structure of the PDF and as much as one third of all white matter voxels in the brain experience orientational heterogeneity. It is hard to model orientational heterogeneity parametrically, and to estimate the PDF without bias a substantial number of additional measurements are required. We discuss non-parametric estimation methods of the important characteristics of the diffusion PDF, and inherent limitations in estimation based on a clinically feasible acquisition protocol. We discuss combining hard and soft shrinkage procedures with a suitable basis representation, and how to construct non-parametric summaries of the diffusion with reduced variance without incurring substantial bias.

This is joint work with Brandon Whitcher, CIC Hammersmith, GSK.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons