Persistent Angular Structure: New Insights from Diffusion MRI Data. Dummy Version

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Abstract
We determine a statistic called the radially Persistent Angular Structure (PAS) from samples of the Fourier transform of a three-dimensional function. The method has applications in diffusion magnetic resonance imaging (MRI), which samples the Fourier transform of the probability density function of particle displacements. The persistent angular structure is then a representation of the relative mobility of particles in each direction. In combination, PAS-MRI computes the persistent angular structure at each voxel of an image. This technique has biomedical applications, where it reveals the orientations of microstructural fibres, such as white-matter fibres in the brain. We test PAS-MRI on synthetic and human brain data. The data come from a standard acquisition scheme for diffusion-tensor MRI in which the samples in each voxel lie on a sphere in Fourier space.